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![](https://rs.olm.vn/images/avt/0.png?1311)
Xét ΔABD có AM/AB=AQ/AD
nên MQ//BD và MQ=BD/2
Xét ΔCBDcó CN/CB=CP/CD
nên NP//BD và NP=BD/2
=>MQ//PN và MQ=PN
=>MNPQ là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
Tứ giác có thể là hình vuông, chữ nhật phải không bạn?
P/s: Hỏi thôi chớ không trả lời đâu :D
![](https://rs.olm.vn/images/avt/0.png?1311)
Xét Δ AQN và Δ MBN có :
\(\widehat{QAM}=\widehat{MBN}=90^o\)
\(AM=BM\) (M là trung điểm AB)
\(AQ=BN\) (Q;N là trung điểm AD;BC và AD=BC)
⇒ Δ AQN và Δ MBN (cạnh, góc, cạnh)
\(\Rightarrow QM=MN\left(1\right)\)
Chứng minh tương tự :
- Δ AQN và Δ QDP (cạnh, góc, cạnh) \(\Rightarrow QM=QP\left(2\right)\)
- Δ PNC và Δ QDP (cạnh, góc, cạnh) \(\Rightarrow PN=QP\left(3\right)\)
- Δ PNC và Δ MBN (cạnh, góc, cạnh) \(\Rightarrow PN=MN\left(4\right)\)
\(\left(1\right);\left(2\right);\left(3\right);\left(4\right)\Rightarrow QM=MN=PN=QP\)
⇒ Tứ giác MNQP là hình thoi (dpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Chứng minh được MBPD và BNDQ đều là hình bình hành Þ ĐPCM.
b) Áp dụng định lý Talet đảo cho DABD và DBAC tacos MQ//BD và MN//AC.
Mà ABCD là hình thoi nên AC ^ BD Þ MQ ^ MN
MNPQ là hình chữ nhật vì có các góc ở đỉnh là góc vuông
![](https://rs.olm.vn/images/avt/0.png?1311)
Trong △ ABD ta có:
M là trung điểm của AB
Q là trung điểm của AD nên MQ là đường trung bình của △ ABD.
⇒ MQ // BD và MQ = 1/2 BD (tính chất đường trung bình của tam giác) (1)
Trong △ CBD ta có:
N là trung điểm của BC
P là trung điểm của CD
nên NP là đường trung bình của △ CBD
⇒ NP // BD và NP = 1/2 BD (tính chất đường trung bình của tam giác) (2)
Từ (1) và (2) suy ra: MQ // NP và MQ = NP nên tứ giác MNPQ là hình bình hành
AC ⊥ BD (gt)
MQ // BD
Suy ra: AC ⊥ MQ
Trong △ ABC có MN là đường trung bình ⇒ MN // AC
Suy ra: MN ⊥ MQ hay (NMQ) = 90 0
Vậy tứ giác MNPQ là hình chữ nhật.
![](https://rs.olm.vn/images/avt/0.png?1311)
Xét ΔMNQ có
A là trung điểm của MN
D là trung điểm của MQ
Do đó: AD là đường trung bình của ΔMNQ
Suy ra: AD//NQ và AD=NQ/2(1)
Xét ΔNPQ có
B là trung điểm của NP
C là trung điểm của QP
Do đó: BC là đường trung bình của ΔNPQ
Suy ra: BC//NQ và BC=NQ/2(2)
Từ (1) và (2) suy ra AD//BC và AD=BC
Xét ΔMNP có
A là trung điểm của MN
B là trung điểm của NP
Do đó: AB là đường trung bình của ΔMNP
Suy ra: AB=MP/2=NQ/2(3)
Từ (1) và (3) suy ra AD=AB
Xét tứ giác ABCD có
AD//BC
AD=BC
Do đó: ABCD là hình bình hành
mà AB=AD
nên ABCD là hình thoi
Lời giải:
$Q,M$ lần lượt là trung điểm của $AD, AB$ nên $QM$ là đường trung bình của tam giác $ADB$ ứng với cạnh $BD$
$\Rightarrow QM\parallel BD$
Tương tự:
$MN\parallel AC, PN\parallel BD, QP\parallel AC$
Do đó:
$MN\parallel PQ\parallel AC$ và $QM\parallel PN\parallel DB$
Tứ giác $MNPQ$ có 2 cặp cạnh đối song song với nhau nên là hình bình hành.
Mà $AC\perp BD$ (do $ABCD$ là hình thoi)
$\Rightarrow QM\perp MN\Rightarrow \widehat{M}=90^0$
Hình bình hành $MNPQ$ có $\widehat{M}=90^0$ nên $MNPQ$ là hình chữ nhật.
Hình vẽ:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZIAAADvCAYAAADYSVJRAAAgAElEQVR4Ae2df4hdR9nH/auQbmLabOKWNFvaNNCkLW/zR+0bm0Dojz9abLS8cStSsdT8LomNoERqoGrUldYaS7WERANikFBJdUmRhrWGpOJSpTZWgppaIi0EQqAtpJhKSp6X71nn7ty5c++de+85Z359D2zOvSdzz5n5PDPne56ZZ+Z8RLiRAAmQAAmQwAAEPjLAb/lTEiABEiABEhAKCSsBCZAACZDAQAQoJAPh449TIXD8uMiaNSK//30qJWI5SKA+AhSS+ljzSgETeOIJkaeeEsGeGwmQQG8EKCS98WLqBAl8+KHI2rUiH3wgMjYmgu/cSIAE3AlQSNxZMWWiBF55ReR735su3K5dIlNTiRaUxSKBighQSCoCy9PGQwBdWr/73XR+Jyenu7jiyT1zSgL+CVBI/NuAOfBI4NIlkQcemB5ox2A7/tC9hePcSIAE3AhQSNw4MVWiBP74R5GdO5sL9/Wvi6C7ixsJkIAbAQqJGyemSpTA00+3hvwiFPiHP0y0wCwWCVRAgEJSAVSeMg4C6L7asKG1GwvH161rPR5HqZhLEqifAIWkfua8IgmQAAkkRYBCkpQ5WRgSIAESqJ8AhaR+5rwiCZAACSRFgEKSlDlZGBIgARKonwCFpH7mvKIHAkePHpUnn3xSdu3aJZOTk3Lx4kUPueAlSSBNAhSSNO3KUv2XwNTUlFx77VJZsOBmWbJku9xww9dkdHSVjI4uEfwfNxIggcEJUEgGZ8gzBEoAQjE0dIWsXDlZzFhXM9exv/32ozJ37lUUk0Btx2zFRYBCEpe9mNseCMATsYmIEhSICTyT8+fP93BWJiUBEjAJUEhMIvyeBAGMiYyMLG/xRJSIqD26uQ4fPpxEmVkIEvBFgELiizyvWymB8fHxYkxECUa7PcZMMADPjQRIoH8CFJL+2fGXAROgkARsHGYtOQIUkuRMygKBwEsvvSTDwzd37dq66qr/lUOHDhEaCZDAAAQoJAPA40/DJPD222/Lo48+KrNnz5cVK460FRMMtg8NzZNNmzbJG2+8EWZhmCsSiIAAhSQCIzGL7gSef/55GRsbkzVr1siqVavk8suHZcUKe/jvnDlXF2mQ9v7775eDBw/KhQsX3C/GlCRAAgUBCgkrQhIE4IXs2LGjEBAIA/72798vx44dK0J8Fyz4H1m8eJssWfJVWbjwE8Wx48ePy89+9rNCRNRvtmzZIm+++WYSTFgIEqiLAIWkLtK8TiUEPvzwwxYx+PKXvyx///vfG9eDl7F3715ZtmyZLF26VJ555pmmuSP/+te/mkQI3skvfvELwbm5kQAJdCdAIenOiCkCJQDPAWMhyptQ3VM2AXj99dcb6fDZth04cEDWrl3bSAdBondiI8VjJNBMgELSzIPfIiHwy1/+summv27dOjlx4kTb3LsICX4M7+QrX/lKQ0zonbRFyv8ggQYBCkkDBT/EQODMmTOyc+fOphs9PIlug+SuQqIYYHwFIqK8HXg+jOxSdLgngWYCFJJmHvwWKIH//Oc/LWMhuLm7dj31KiTAAOFA95YSE+whWsgLNxIggRkCFJIZFvwUKAF4IfpYCMYx0LXVyw29HyEBDoy3QDxUSDHEhN5JoBWF2fJGgELiDT0v7EJAnxeCm/jGjRubIrJczoE0/QqJOj/GTnTvBGKGyK5exEydi3sSSI0AhSQ1iyZSHnRZ2eaFdBsLaVf8QYUE54V3AvHQx062bt3KsZN20Hk8GwIUkmxMHUdBbTdrdCWdPHlyoAKUISQqA/BOICBq7ATCwrETRYf7HAlQSHK0eqBlts0LwViIbV5Ir0UoU0hwbTV2os87gbhAZLiRQG4EKCS5WTzQ8trmheDmX9ZWtpCofNnmnWDNLo6dKELc50CAQpKDlQMuI27E5rwQrH/V71hIu6JWJSTqehAPfewEA/Ocd6LocJ86AQpJ6hYOtHzoGjIXTOxlXkivxapaSJAfc94JhIUrCvdqKaaPkQCFJEarRZ5nzAuxLUNSZXdQHUICs0AgTe8EZeXYSeSVltnvSIBC0hEP/7NsAua8EKyRhZt81VtdQqLKYfNOygocUNfgngRCIUAhCcUSiecDy7qbXgjWsyp7LKQdxrqFBPmAd2LOO8H7TvQl7tvll8dJICYCFJKYrBVhXlVXjx4mC0FxXSOrrCL7EBKVd3Rr6Uu8YOwE40NVduWpa3NPAnUQoJDUQTnTa9jmhezZs8fLDdSnkMD8tuACCCre7MiNBGInQCGJ3YKB5n9iYqLpfSGYrOezS8e3kCgzQVzNLj56J4oO97ESoJDEarlA841BZn2NLHTjhPDa2lCERJkN4qGWWMEeQlt3d5/KC/ckMCgBCsmgBPn7goCt6wYRWT69EN00oQkJ8mbr+ut1eXy9jPxMAr4IUEh8kU/oupgXonsheMLGE3ddEVkuKEMUEuTbFtnV71L5LhyYhgSqIEAhqYJqRuc054Wg/z8UL0Q3Q6hCovJozjuBGIfQJajyxz0JdCJAIelEh//XlgDEQn/RE258+/btK56w2/7I43+ELiQKDWbFg6X68xEqrfLCPQm4EqCQuJJiuoKAbV5IDJPsYhESQIZIm/NOMHmT807YCEMlQCEJ1TIB5gtzHszQVXRtxXCDi0lIYHoIthlCDcFGFxg3EgiNAIUkNIsEmp8XXnhBxsbGGl0ueGIOcSykHb7YhESVA4zNtzFy7ETR4T4UAhSSUCwRaD4QkWW+L6TONbLKwhKrkKD8qjtRf98J552UVTN4njIIUEjKoBjoOV599VVBKOk999xT7F977TXnnKqwVN0LwbkGfXe6cwZKThizkCgUtnkndXsnmzdvlsOHD6ssFXt4q+h245YvAQpJorbHTedzn/tc48YPEfnsZz8r//znP7uW2DYWgjWyQpoX0rUQRoIUhARFsnkniJ6D51jHdvfdd8tDDz3UiM5DflDPcJxbvgQoJIna/rvf/a789re/bSrdiy++KDjeacPMat0LSaULJRUhUbYzvROsrlyHdwLBGB8fl6mpqSIrr7zySlGnKCTKMnnuKSSJ2v3Tn/60XLx4sal0+P6pT32q6Zj6Ai/EnJ0euxeiyoZ9akKCMsEbwHiVPnZS5euKcU0IxuTkpOzdu7fAi7lD6NqikBQ4sv2HQpKo6TEuYttsx00vBP3dJ06csP082mMpCokyhumdVLlQJgQDDx3wVLFt27atWDOMQqKskeeeQpKo3eGRmPM7PvjggyaPxOaFPPvss/L+++8nRyVlIYGxbN5JFWMnSjA+85nPyDvvvCP33XdfUVfU8eQqDgvkRIBC4oQpvkQYCzly5EiRcXgcP//5z4vvaozE5oXEGpHlYp3UhUQxwNsY9aVrMHaCSaMQmjI2JRjf+ta35Pvf/75885vfLE6rjpdxDZ4jPgIUkvhs5pTj06dPF1FaEAd4Htu3b5cHH3xQ/vCHP7SMhYS2Uq9TAXtMlIuQAIvNO8GKBBCZQTclGL/+9a+LF5c999xzxSnV8UHPz9/HSYBCEqfdnHL9l7/8pTGP5JlnnpEf//jHcu+99zZmp2MsJGUvRIeUk5Cocpvviod3Ak90EO9ECcapU6eKAXZwxaaOq2tznxcBCkkG9sYNRS2z8clPfrIQkhy8EN20OQoJyo+5P4is0iO7yvJOdL78nDcBCknC9seTJ+YW6DeRnLwQ3bS5ColigMgu9TCBJerL8E7UubknAQpJonVA90Jw44CY5OaF6KbNXUjAAt7JgQMHmh4s6J3otYSf+yVAIemXXAC/++tf/yq7d+8uZhq//PLLRY5sXgieRMsYaA2gyH1ngUIygw4rCmPdNPXyLNM7sdWrmV/zEwm0EqCQtDIJ/ghmqK9cuVLmzp0rixcvLv7mzZsny5cvl/Xr1zduEFVOTAsekpFBCkkzEDxwmN7JI488IrfeemtLvbrtttvk3LlzzSfgNxLQCFBINBixfISIjI6Oyh133FFEyyBi5q677pJFixbJ8PBwMUmMXkizNSkkzTzUN7woS72Ncf78+bJw4cKWeoW6BjExl9xR5+CeBCgkkdUBrOILT0QXEQiJEpOhoaFiSW8scYKbJ/+mGRw6dEhWr15d/OEzuczUDbxuAGIya9astvUKHq/qPo2syTC7NRCgkNQAucxLYEzk+uuvb3giSkTUHk+Py5Yta3RvqX7w3PcQkZGRkeIPn3PnYZb/pptuKjxaVY/MPbpQseovNxKwEaCQ2KgEfAxCgkZtNnT1nUKyxioSFBI7FyUo3YTkuuuuo5AEfF/wnTUKiW8L9HB9DJDiqbBTF8SVV15ZhPmy62am6wYs2LXVzMOsH1jqZM6cOW27tmbPni2PP/74QLPie6jqTBoZAQpJJAZDyKaaUKYGRe+8886GZ4LB9muuuYaDom3siRunevrGZ26tBFQQh1mv4OUyiKOVF4/MEKCQzLAI8hOWgsdEQn12+oYNG4owTTxBIlILDR2eCCJrsFgjt1YCFJJWJuaRd999twgrN+vVLbfcIg8//HBDiBlWbpLjdwpJwHVA90LwNG02YHRHoG8bg+sQG4ZntjcmhaQ9G/N/bPWKE11NSvyuE6CQ6DQC+WzzQmxLWfDm6G4wsiqHFVZI0N93Yj7cuF+FKVMiQCEJzJqmF2IuX6FnlzdHnUbnz2TVmY/+v91YqVnxY2Njje4ujN/l8koCnRU/TxOgkARSE+CF7N+/v2ksxOaF6Nnt1uD1tLl/Jiv3GuDKylwYFN2vOS8M6k44vZQUkgBsqi9TgcbYyQvRs+va4PXf5PqZrNwt3wsr29hJrq8qcCecXkoKiUebohHijXUQDhWa2s0L0bPbS4PXf5fjZ7Jyt3o/rPA6Z33shN6JO+8UUlJIPFnR1i2A1VghLq5bPw3e9dyppSMrd4v2ywrds3iRmv5gRO/EnXvMKSkkNVtPeSH6QCUWzMMge69bvw2+1+ukkJ6s3K04KCs8JEFAlJeNPQSml4ck99wyZQgEKCQ1WgGvO1VLdqNxDRo6OWiDr7Ho3i9FVu4mKIMVRGNiYqLJO0HXF8YDuaVHgEJSg03RqBCRpbv8CJeEsAyyldHgB7l+TL8lK3drlckKdRzjfso7wcPTwYMHi9f+uueIKUMnQCGp2EJnzpyRHTt2NBoSxASiUoabX2aDrxiD99OTlbsJqmCFoBK9OxcPUvRO3G0SekoKSYUWev7555saD1z7Qb0QPbtVNHj9/Cl9Jit3a1bFCpFd5kMVBKaMhyr30jFlFQQoJBVQxZOW6c5johaiWsrcqmrwZeYxlHORlbslqmZl8044K97dPiGmpJCUaBU8WSGEF/3Aqk8YLjyiWKrYqm7wVeTZ1znJyp18HaxM7wTtBWMnZT9suZeaKQchQCEZhJ7227Nnz8rOnTsbAgIxqXq5iDoavFbEqD+Slbv56mRl8076CYV3Lx1TVkGAQjIgVXgheJIyBxLraAx1NvgBMXn/OVm5m6BuVjbvBOOLHDtxt5nvlBSSASxgmxeCrq263PO6G/wAqLz/lKzcTeCLlemdcN6Ju818p6SQ9GEBCAW6rfR5If3OTu/j8o2f+GrwjQxE9IGs3I3lk5XpnXDeibvdfKakkPRIH/NCzIgsX8s/+GzwPWLznpys3E0QAivTO+G8E3f7+UhJIemBujkvxHflDqHB94DPa1KycscfCiubd+Lroc2dXp4pKSQOdsdYiDmRChW6rrGQdlkMpcG3y19Ix8nK3RqhsUJbqyuk3p0SU+oEKCQ6DeMzokYwFqJXYoyFhLK0Q2gN3sAX1FeycjdHiKzM1y6osRPfD3PuVNNOSSFpY1/MC9G9EFRcrJEVUsUNscG3wen9MFm5myBUVniws3kndYTau9PLMyWFxLA7KqttoK/MNbKMS/b9NdQG33eBKvwhWbnDDZ2V6Z1gVnyvL4Vzp8GULgQoJBol27yQslbq1S5T2sfQG3xpBS3hRGTlDjEGVjbvhPNO3G1cdkoKyX+JwgvR54WgUobuMsfQ4MuusP2ej6zcycXEyvRO0AVN78Td1mWlzF5IUBFta2SFNBbSztgxNfh2ZajrOFm5k46NFb0Td9tWlTIqIVmzRkT/u/9+kVdf7Q8NKp8tIit0L0QvbWwNXs973Z/Jyp14rKxs3onPeSfmverRR0VOnXK3Q0wpoxMSHS5EZO3a3sWk3ez0GLwQvfyxNni9DHV9Jit30jGzsnknVb7KoRNVCInaLl0SmZwU2bxZHUlrH7WQwBQQE3gmrps5O33dunWChhPjFnODr5s3WbkTT4GVzTvBOCiEpq5NFxJ1TTz4prhFLyQwis1gprHQZWWukYWIrAsXLphJo/meQoOvCzZZuZNOhZXNO9myZUttQTTmfemll0R+9St3O8SUMnkhQWXC+0L0iCwISojzQnqtOKk0+F7L3U96snKnlhoreCdYkUK9tRSRXRgfrborG0Ji/k1MuNshppRJC4ltXsiePXsqr0B1VYDUGnyV3MjKnW6KrPBAaQbX4IESC0NWtZkeyRtviHz+81Vdze95oxeSdmMkExMTTV4IBtxiishyqRYpNniXcveThqzcqaXMCg+XZhd3Vd6JKSSwwP/9n7sdYkoZtZD86U/TUVvYqw0LKpprZPkMAVT5qmKfcoMvmxdZuRPNgRXEQ3V1YY8HzbK7u00hefFFkccec7dDTCmjExK9z1GfR2JzXRGRlZoXoleuHBq8Xt5BPpOVO71cWNm6vhHZVdbYiXmvgoicPetuh5hSRiUk7cBiXojuheAJA08cMUdktSurfjyXBq+Xud/PZOVOLidWtsiujRs3Jv0A6l4T3FNGLyTmvBD0f6bsheimzanB6+Xu5zNZuVPLkRW6xLG+nt7dlWqXuHtNcE8ZrZBALEzD79u3r9YJR+6Yq0mZY4PvlyRZuZPLmRWmCuhikspUAXfr95cyOiGxzQupc5JRf5ir+VXODb5XomTlTix3VnhINeedhPZSO3dr1pMyOCE5evSoPPnkk7Jr1y6ZnJyUixcvNkiYa2ThySGleSGNgjp+yL3BO2IqkpGVOy2ykqJnA+OsY2NjDQ8FPSBmZFen+5U78fhTBiMkU1NTcu21S2XBgptlyZLtcsMNX5PR0VUyOrpE8H/mWwvhhZw8eTJ+CwxQAjZ4d3hkRVbuBGZSmpFdWCEDYyfHjh3reL+aOUMen4IQEgjF0NAVsnLlZMuSArffflRmzZonq1atajwZYCwk9Ygsl+rHm6MLpek0ZEVW7gSaUyIcGOKhllnCveiyy4ba3q/mzr2qePhtPkva34IQEngiNhFRcdgQk6GhebJ+/fpsIrJcqh1vji6UptOQFVm5E7CnhHeCnpDZs+fLihVHWh569fsVelLOnz9vP1GCR70LCfoYR0aWtzWKMs6CBR+Xp556qljyHTcF/r0uhw4dktWrVxd/+Ewm7esFWbVnY9YbsmrPau/evTJv3k1d71folj98+HCCkmEvknchGR8fL8ZElGC02y9Z8lVZunRpo3tLD9HL9TNEZGRkpPjD51w5uJSbrNY41w+yas9q2bJlsnjxtq5CgjFeBAzlslFI1rSvNC43KJ9p2ODdbUdWZFVGW6WQ2KXRu5C4dm197GMflx/84AfsvtG69dgF0b4Lgt017mzIyp3VT37yE7nyyhu7eiTs2rILTqVHXQfbN23aJFjKgNs0AdwA1FMWPnNrT4Cs2rMx/4esTCLT3/HuEkxU5GB7Kx/vHgmyhPDf4eFFsmKFPfx3zpyrG+G/eLsZljFg+K8U3hmFpLVS247w5mijYj9GVq1c9DX9EP57+eXDbe9XIyPTc99az5LukSCEBHghJgiZQwSXOSHx+PHjLW83QxieOcs0XTPZS8YGb+diO0pWNir2Y2Q1wwVeiLmyOJZLwYTEdvcr3Mty24IREoCHl4FlURDJhYgHhM/psdh497JuVHgnOa/QyQbv3lzJiqzcCcwskYJ7jPL6sUSKvrJ4t/tVL9eLPW1QQuIK88CBA41ZpjCybQ0c13PFnI43R3frkRVZuRIwl0VR3elYMJabnUCUQoKiwDsx372cm3fCm6O9UtuOkpWNiv1Yzqywpp9aCgUPqXjL6okTJ+ygeLRBIFohUSVAf6XufiKqIpfIrpwbvLK/656sXEnlGcSBlcV37tzZ6MbCPQU9Hwzqcas30QsJiml7uxkqQVnvXnZDWX8q3hzdmZMVWdkI4B6B5eLNh9HcA3lsrDodS0JIUED0X0I89PcHpO6d8ObYqWo3/x9ZNfPo9C0XVvBC9BdYoUsLXVupP4B2sn2//5eMkCgAGDvRX8Gr3h+QYuXIpcEr2w6yJyt3ejmw0ueFYCxk48aNTRFZ7rSYEgSSExIUCt4JBt51d3Xr1q3JjZ3k0ODLaqZk5U4yZVbostKnEEBEMM7KsRD3+mFLmaSQqILCO4GAoLLgTw2gpeKdpNzglQ3L2pOVO8kUWdkeLtGtlftbVt1rReeUSQsJiq7GTvSQPogLRCb2LcUGX5VNyMqdbGqsbPNCMBaCewO3cggkLyQKk23eCdbsitk7Sa3BK1tVsScrd6opsbLNC0H5uJVLIBshUdggHvrYCQbmY513klKDV/apak9W7mRTYIUHR3NeCMJ8ORbiXg96SZmdkACOOe8EwhLjisIpNPheKusgacnKnV7MrNBdxXkh7rYuK2WWQgJ4qHCmd4IlV2IaO4m5wZdVgV3PQ1aupOKd2Y55IbZlk2Luvna3mt+U2QqJwm7zTmIZiOPNUVmx+56sujNSKWJkZc4LwRpZKAe3eghkLyTADO/EnHeC953oS0bXY47erhJjg++thOWlJit3ljGxQhs1vRDOC3G3dVkpKSQaSXRr6UsmYOwE/a2husYxNXgNs5ePZOWOPQZWqmtaD+uHoHCNLHc7l5mSQmLQtA3WoYLiTWmhbTE0+FCYkZW7JUJnZZsXsmfPnmAf+NzJx5uSQtLGdqispsscmncSeoNvg9bLYbJyxx4yq4mJiab3hWBycehd0O7k401JIeliO4iHWmIFe1TcUNznkBt8F6y1/zdZuSMPkRWCYvQ1stDtnNuL7NwtWH9KCokDc5srHcJy0yE2eAecXpKQlTv2kFjZupoRkUUvxN2edaSkkDhStkV2+V56OqQG74jRWzKyckcfCivMC9G9EPQIoIeAs9PdbVlXSgpJj6TNeSeo3L5c7FAafI8IvSQnK3fsIbAy54VgvJJeiLsN605JIemTOGbF62MnPkIPQ2jwfeKr/Wdk5Y7cJyuIhf5iOrSxffv2caVed/N5SUkhGQA7Kr057wSToeqad+KzwQ+AzctPycoduw9WtnkhMUwKdqeadkoKyYD2RQMwQxLRANAFVvXmo8FXXaaqzk9W7mTrZoU5WmaoPbq26nogcyfDlO0IUEjakenxOLwT822MVY+d1N3ge0QSVHKycjdHnaxeeOEFGRsba3QTw8PnWIi7rUJJSSEp0RLKPdffd1LlvJM6G3yJmLyciqzcsdfBChFZ5vtCuEaWu41CS0khqcAitnknVXgnnRr83XffLerv3nvvFYQqnzp1qoLSxnHKTqziKEF9uezECnXqyJEjLZnBcZdNhdHrXgjqJt+d7kIv3DQUkopsY/NOEI2CJ7Gytm4NXr/O5OSkbN68WT+U1edOrLIC4VDYTqwgGOh+eu+995rO5CIktrEQrJHFeSFNKKP8QiGp2Gymd4LVSsvyTro1eLNo8Exy3TqxypVJu3J3YgXB+Nvf/ibf+c53mn7eTUiwEoTuhVTZ5duUMX6phQCFpAbM8E7Q/6uPneCpbtA1u7o1eFW0S5cuFZFl27ZtU4ey23dilR2MLgXuxEoJxo9+9COZmppqnEkdbxz47wd4IebsdHohJqX4v1NIarSh6Z0MuvBctwaPxo2/e+65R7Zv3y5vvfVWjaUN61KdWIWVU/+56cRKCca///3vIkoRe2zquJ570wtBWPyJEyf0JPycCAEKSc2GtHkn/Y6duDT4mosX7OU6sQo2054y1omVLhjwSOCZYNOP27yQZ599Vt5//31PJeJlqyZAIamacJvz422M+lIQGDvBJCwIjevm2uBdz5dyuk6sUi53P2XrxEoXDJwbYyUYM1HHbV4II7L6sUJcv6GQeLSXzTvBDF+IjMvWS4N3OV/KaTqxSrnc/ZStEyslGOq8iN7CeB+Om2MhXKlXUUp/TyEJwMbmu+LhneDJrpt30kuDD6CYXrPQiZXXjAV48U6sTCFBHf32t79dCIlaxBRjIfRCAjRshVmikFQIt5dTI5Yeq5zqkV3dvJNODb6Xa+eQlqzcrezKCg9A+rJAEBJ6Ie6cU0pJIQnMmojs0htnJ+/EtcEHVkQv2SErd+zdWMELwVwo/aGHXog73xRTUkgCtCq8kwMHDjQ1VJt30q3BB1g0b1kiK3f0nViZXgjEhF6IO9tUU1JIArYsVkHFOkSq79n0ThDlddNNN8myZcuKxhxwUbxnrdPN0XvmAsuArV7ZvBB4zq6BIYEVkdkpmQCFpGSgZZ8ODdj0Th555BG59dZb5aMf/ahcffXVMjo6KldccYXcdtttcu7cubKzkMT5KCTdzXjx4kVZuXJlS71avny5rF+/vvFAM+hE2u45YYrYCFBIIrEYXpSFMEt4J/Pnz5eFCxfKHXfcUUTLIJLmrrvuKgQFYoIbArdmAhSSZh62bxARPJSY9WrRokUyPDws9913XzF+Ry/ERi/vYxSSiOyPN8aNj4/LrFmzmho7hESJCTwT9Fnjxsm/GQaHDh2S1atXF3/4TDYzbMDiueeekzlz5rStV0NDQ/L44493DUmPqDkxqyUSoJCUCLOOU+3evVuuu+66hieiRETt8USJMRM1rsL9moIFRGRkZKT4w2dymeaiOGCsDZ6HqkfmHnUODzHcSMBGgEJioxLwMQjJ9ddf37bBU0iab5DqRkkhsXNRfLoJyeLFiykkAd8XfGeNQuLbAj1e/6PVShYAAAkTSURBVLXXXpO5c+e27YKYPXu2qFVW2X0z033Drq0ZFma9wIq8GH/r1GWKMZKXX365x9rK5LkQoJBEaGk1KHrnnXc2PBM12M5BUbtBcfNUT9/4zG2aAELM1QRYFcRh1qtrrrmmiAhkEAdrTTsCFJJ2ZAI+/u677xZhmvBM0OWAPwjILbfcIg8//HDjhskwzRkjUkhmWOATAjcQlKHPTt+wYUMRVm7WK0QCnj59uvkE/EYCGgEKiQYjto/o5sKYCQZB0e2AJ0ZOHLNbkUIyw0X3QuClmQ8ctno182t+IoFWAhSSViZJHEGsv/6+E/NmkUQheygEhcTuhdiW3ukBK5OSQEGAQpJwRVCz4sfGxhrdXegPz3GJ79yFxPRCzOV2Em4GLFoNBCgkNUD2fQlzoT10Z+S20F6uQoKxkP379zeNhdAL8d0i07s+hSQ9m1pLZBs7yWnp7xyFRF9WBw8P9EKsTYMHSyBAISkBYkynePvtt5vGTnLxTnISEjw04A2bEA7YF3/0QmJqpfHllUISn80GzjG6O/BiIv1Gk7p3kouQ2LoxsXo0xIUbCVRFgEJSFdkIzoubDgREPbViD4FJ8aaTupAoL0QPrMBsdQyycyOBqglQSKomHPj5cQOamJho8k4QNoz+9ZS2lIUEr2dWrxjAw0Duod4p1dtYykIhicVSFecTNyP0oyvvBDejgwcPCl77m8KWopDgIQARWXoXJcK7YUtuJFAnAQpJnbQjuBYGafXuEdyYUvBOUhOSM2fOyI4dOxrCDzGBqKTYLRlBs8k+ixSS7KtAKwBEdpk3KQhMzDeplIQE71TXxR5dkfRCWusxj9RHgEJSH+vormTzTmKdFZ+CkMAzNLsfMbEUUXjcSMAnAQqJT/oRXNv0TjCGgrGT2G5eMQsJPEGE8GLcSo1hocsRUXfcSCAEAhSSEKwQQR5s3klMoaWxCsnZs2dl586dDQGBmOS2vE0EzSP7LFJIsq8C7gBs3gn662MYO4lNSMAUnp8+FgIvJCbxdq9ZTBk7AQpJ7Bb0kH/TO4lh3klMQmKbF4Kurdi6Ez1UTV7SEwEKiSfwsV/W9E5Cn3cSg5BAKNBtpc8L4ez02FtKHvmnkORh58pKaXonoc47CV1IMC/EjMhKdbmayiojT+yNAIXEG/p0LmzzTkK7CYYsJOa8kFDFOJ0ay5KUTYBCUjbRjM8H8Qg1RDVEIcFYiDnxEww5FpJxI4q06BSSSA0XarbNZczV2Invm2NIQoKILIyF6KKLsZAUlqIJtV4yX9USoJBUyzfLs+NGafNOfIauhiIkmBeieyEQE6yR5Vtos6yoLHRpBCgkpaHkiUwCpneCWdm+XrLkW0ggrrbABK6RZdYafo+RAIUkRqtFlGebd+Jj3olPIbHNC+FKvRFVYma1KwEKSVdETFAGAdM7QZdOnd6JLyGBF6LPC4GI+uziK8OWPAcJmAQoJCYRfq+MgE/vpG4hgXDa1sjiWEhl1Ysn9kiAQuIRfq6XtnknVc876SYk//iHyGOPiaxdK7J3r8g77/RnHYilLSKLXkh/PPmrOAhQSOKwU3K5tHknVS6N3klI3npL5ItfFHn1VZFLl0Tee0/kG98QefHF3rC3m51OL6Q3jkwdHwEKSXw2SyrHNu8E4woQmjK3TkLyxBMik5PNVzt3TuTpp5uPdfpmzk5ft26d4JrcSCAHAhSSHKwceBlt3smWLVtKHZTuJCQPPCDywQf9QUKXlblGFiKyLly40N8J+SsSiJAAhSRCo6WaZXgnmOGt3gKIyC6MN5TRNdRJSO6/v3eiED+8L0SPyIKgcF5I7yz5i/gJUEjit2FSJcAN2hysxg0aC0MOsnUSkgcfFLE5ELZjyINtXsiePXtKEbxBysjfkoAvAhQSX+R53Y4EcLM2u4wG8U46Ccnu3a1jJG++KbJpU2sWJyYmmrwQvrWwlRGP5EeAQpKfzaMqMcRDdXVhjxt3P91HnYTk9GmRL3xB5M9/nkYD52frVpHf/GYGFRZUNNfIqjpkeebq/EQCYROgkIRtH+auTVcSIrt6GTvpJCSADBH50pdEMF7y0EMiExPT6G1dbYjI4rwQVk0SmCFAIZlhwU8BE7BFdm3cuNH5ht5NSGxFx7wQ3QuBRwQPiRFZNlo8ljMBCknO1o+w7OhiwnpVeneXSxdTr0JizgvBeA29kAgrDLNcCwEKSS2YeZGyCSD0VheTbqG3rkICsTCFat++faVPkCybB89HAj4JUEh80ue1ByKAm74576TdS6K6CYltXkjZkyIHKix/TAIBE6CQBGwcZq07ATUYPjY21vBQ4FGYkV0//elP5cYbb5SlS5fK3r175eLFi42Tm2tkwdPhvJAGHn4gga4EKCRdETFBDATMSYKYcY6xk2PHjsm11y6V4eEbZfHibbJkyVdl4cJPyOjoEpmammp5ayG8kJMnT8ZQZOaRBIIhQCEJxhTMyKAEEA4M8VDLlqxatUouu2xIVq6clDVrpOnv9tuPyqxZ8wRp1FgLxkIYkTWoFfj7HAlQSHK0euJlhncCz2L27PmyYsWRJgHRBQViMjQ0T9avX8+IrMTrBItXLQEKSbV8eXZPBCYnJ2V4+Oa2IqIEZWTktqJ7y1M2eVkSSIIAhSQJM7IQJoHx8XFZsmR7VyG54Yavya5du8yf8zsJkEAPBCgkPcBi0ngIUEjisRVzGj8BCkn8NmQJLASOHj0qIyPLu3oko6Or5PDhw5Yz8BAJkIArAQqJKymmi44Awn5tEVtqfASD7QgDPn/+fHRlY4ZJICQCFJKQrMG8lEoA80SGhxfJihX28N+Rkem5JKVelCcjgQwJUEgyNHpORYaYwOtANxcG3zG4ju4sNSExJxYsKwlURYBCUhVZnjcYAphkiHBgDMAjQgtjIuzOCsY8zEgCBCgkCRiRRSABEiABnwQoJD7p89okQAIkkAABCkkCRmQRSIAESMAnAQqJT/q8NgmQAAkkQIBCkoARWQQSIAES8EmAQuKTPq9NAiRAAgkQoJAkYEQWgQRIgAR8EqCQ+KTPa5MACZBAAgQoJAkYkUUgARIgAZ8EKCQ+6fPaJEACJJAAAQpJAkZkEUiABEjAJ4H/B6Fp3mZ3lxgQAAAAAElFTkSuQmCC)