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![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(BC=BH+HC=3,6+6,4=10\left(cm\right)\)
Tam giác ABC vuông tại A, đường cao AH có:
\(AB^2=BC.BH\\ \Rightarrow AB=\sqrt{BC.BH}=\sqrt{10.3,6}=6\left(cm\right)\)
Tương tự:
\(AC=\sqrt{BC.CH}=\sqrt{10.6,4}=8\left(cm\right)\)
Ta có: \(AH^2=BH.CH\)
\(\Rightarrow AH=\sqrt{BH.CH}=\sqrt{3,6.6,4}=4,8\left(cm\right)\)
b) Tứ giác AEHF là hình chữ nhật (tứ giác có 3 góc vuông) nên EF = AH = 4,8 (cm)
c) Tam giác AHB vuông tại H có EH là đường cao (gt) \(\Rightarrow AH^2=AB.AE\)
Tương tự tam giác AHC ta có \(AH^2=AC.AF\Rightarrow AB.AE=AC.AF\)
Xét tam giác AEF và tam giác ABC có:
\(\widehat{FAE}.chung\)
\(\dfrac{AF}{AB}=\dfrac{AE}{AC}\left(vì.AB.AE=AC.AF\right)\)
Do đó tam giác AEF đồng dạng tam giác ABC.
![](https://rs.olm.vn/images/avt/0.png?1311)
c: Xét ΔAHB vuông tại H có \(AE\cdot AB=AH^2\)
=>\(AE=\dfrac{AH^2}{AB}\)
Xét ΔAHC vuông tại H có HF là đường cao
nên \(AF\cdot AC=AH^2\)
=>\(AF=\dfrac{AH^2}{AC}\)
XétΔABC vuông tại A có
\(tanC=\dfrac{AB}{AC}\)
\(\dfrac{AF}{AE}=\dfrac{AH^2}{AC}:\dfrac{AH^2}{AB}=\dfrac{AB}{AC}=tanC\)
=>\(AF=AE\cdot tanC\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ABC vuông tại A có AH là đường cao
⇒AH² = HB . HC
= 4 . 9
= 36
⇒ AH = 6
Tứ giác AEHF có:
∠HEA = ∠FAE = ∠AFH = 90⁰
⇒ AEHF là hình chữ nhật
⇒ EF = AH = 6
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,AC=\sqrt{BC^2-AB^2}=16\left(cm\right)\left(pytago\right)\)
Áp dụng HTL: \(AH\cdot BC=AB\cdot AC\Leftrightarrow AH=\dfrac{192}{20}=9,6\left(cm\right)\)
\(\sin\widehat{B}=\dfrac{AC}{BC}=\dfrac{16}{20}=\dfrac{4}{5}\approx\sin53^07'\Leftrightarrow\widehat{B}\approx53^07'\)
Lời giải:
a. Áp dụng định lý Pitago:
$AC=\sqrt{AB^2+BC^2}=\sqrt{12^2+16^2}=20$ (cm)
$DH=\frac{2S_{ADC}}{AC}=\frac{AD.DC}{AC}=\frac{16.12}{20}=9,6$ (cm)
$AH=\sqrt{AD^2-DH^2}=\sqrt{12^2-9,6^2}=7,2$ (cm)
$HC=AC-AH=20-7,2=12,8$ (cm)
b.
Dễ thấy tứ giác $DEHF$ là hcn do có 3 góc vuông $\widehat{D}=\widehat{E}=\widehat{F}=90^0$
$\Rightarrow EF=DH=9,6$ (cm)
c.
Áp dụng hệ thức lượng trong tam giác vuông cho tam giác $ADH$ và $DHC$:
$DE.DA=DH^2$
$DF.DC=DH^2$
$\Rightarrow DE.DA=DF.DC$ (đpcm)
Hình vẽ:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWoAAADoCAYAAADG166EAAAgAElEQVR4nO3de1iUZf4/8DcwDAPIQcXUNTNDTUtSDhmesDSzzPGyPJRarWtqZu3P3XY3r1L3i+Xm99tX283Nw+6ahxIz/YolhqbWghYBIipJFiRltgYqyEFgYGDm98c0E4c5wjPz3PPM+3VdXV3OfOZ5PrfDfBzu+/48D4x2ZGRk2HvaorKyUug4XxqH6GMwGpUxDl/6mXLHeTkO62yNwx9ERCQ0FmoiIsGxUBMRCY6FmohIcCzURESCY6EmIhKcqqqqym6Ao+cBoLa21qmTyRUH+M44vGEMgDLG4Ss/U+44r2jj8PPzg9FodPm8nhqHKiIiwu6LHD3POPHiRM7NlVjRx8E4xnkqjlMfRESCY6EmIhIcCzURkeBYqImIBMdCTUQkOBZqIiLBsVATEQmOhZqISHDsTHTjedmZaJsSxuErP1PuOK9o42BnIuM8Hidybq7Eij4OxjHOU3Gc+iAiEhwLNRGR4FioiYgEx0JNRCQ4FmoiIsGxULcQFhYmdwpE5Eau7EwSiUruBOSm0wH/8z/AqVNAcrI/4uLkzoiIpLJxI3D4cPvH+/QB1qwBIiM9n1NH+Pw36p9+Amprgfh4IC3NVLiJSDni44E9e4ADB375LyYGeOkloLJS7uyc47OdiUFBQQgKCsKhQ34IDQUmTgQ2bDAV7r59m1BfXw+DweCR/NiZ6P7zitYJJ0ocoMxxhISEIDAw0GbsQw8BX34JXL8OhIU1Q6fToampyW35sTOxE3GVlaY3a/Jk4I47gPBw4Nw5oH9/lcP5apHGIcI5XYlzNlb0cTDO++KMRiP8/PxaPRYQEIDQ0FAh8rMV59NTHyUlQHU1MHSoaa4qJgbIz+f0B5FSmYv0oUOmL2j9+8uckJN8ejExOxsYNAjo3dv058REIDkZ+OorcFGRSCFOnQJmzWr/+IMPej6XjvLZQv3dd8DnnwN/+AOg0Zgeu+MO08JDdjYLNZFSxMcDy5b98jkHTBsH/vUv05czb/is+2yhPncOqKkxfYNuq08f0/y1t2zdISLXTJxomub0li9lPlmodTrTm/Tgg8CSJa2f++47YMUK0/y1N7yBROS8hoYGBAUFyZ2Gy3xyMfGnn4CiItOvPW317m2at+aeaiLlUavVrf7ct69MibjIJwv1oUOmrXi33db68cbGRmg0pm/SRUWmgk5EymHe9XH0KFBaCowdK3NCTvK5qQ/z3umYmPZz0E1NTVCr1Rg61PRn055qz+dIRNKxtuvD21rIfaozUaVSITw8GJs2mX6RMBqN0Ol0aGxsBADU19cjMDAQ/fsHIiXF9Dq9Xo/6+nqh76fmznOyM9E2JX02PH1ed49DrVZDo9FgyRK/dutQLTU1NUGn08FgMAj9GffpzkQ/Pz8EBwcjODjY8ljbttPAwECrragijUOEc7oS52ys6ONgnPfFNTc3IyAgwPJnlUqFLl26CJOfrTifnKMmIt9048YNuVPoEBZqIiLBKXoxMS8vD/n5+SgqKkKXLl0QHx8vd0pEJLG8vDykpaXhm2++QXx8vCI/54os1HV1dUhKmoKyMj38/e8AALz//u/Qr18XHD/+Efz9+YsEkbdr/zk/BYPhXUV+zhVXqOvq6hAT8xB69kxGbOx9rZ67cuUwhg4dj4KCY1CpFDd0Ip/ha59z5fyT87OkpCno2TMZUVH3tXvuppseRHDwM5g69SkZMiMiqfja51wZ/9z8LC8vD2Vlje3+hW2pT5/ZOHt2Kz788EPc1qY18caNGza36ogQV1JSgm7dugmZm7NxgDLG4cwY5MxPyeMoLCzE5cs6JCTY/5wXFr6D8+fPY8iQIQ7PIzpFFer8/Hz4+9/pMK66ugZLly7FXXfd1epxvV5v9/Y9cseVl5dj//79QubmbBygjHE4MwY581PyOC5evIjAQCsX6mmjouI63nrrLWzYsMFhrOhUmZmZdgMcPS+SoqIiJyONaGhoQHl5uVvzcQdvzNkaJYxDCWMAvG8czu+FNqK0tNSpGhYZGYlKQe50ay1f1bhx4+y+wN7zZlVVVU513bg7rkuXLtiz5/cOX6fRqPH6669j+PDhrR4X6dc7a/Ly8pCQkCBkbq5MfShhHM6MQc78lDyOr776Ci+8sN7ha3v06IbVq1e3mvoQpVbZYqvmKmrqIz4+Hr16BeHq1WPo0eN+qzE//rgTAQHXceDAAQQFBeHRRx+1rAyL/iZWVFQgJiZGyNycjQOUMQ5nxiBnfkoeR0xMDNat2+Lwc3777VGKmJ8GFLjrIzPzACoqVuPq1aPtnisrO4jy8jeRmDgYDQ0N2LlzJ5YsWYL8/HwZMiWijnL0OdfptuDDD3fIkJl7KOobNQAEBwfj7NnDGD9+Kk6eXAG1ehgAQK8vwKBBPXDx4klcu3YN//znP5GdnY3S0lIkJycjMTERjz/+uEsXFiIieTj6nOfkZMicobQU940aADQaDbKyjmD9+j8iMjIHgYGf4m9/ewEZGWkAgKioKLz88stITk5Gr169AADZ2dl44YUXsGfPHjQ1NcmZPhE5oeXnPDDwU0RG5rT6nCuJIgu12eDBg9GvXz/07NnT6lxVXFwcNm7ciCeeeAJBQUGcDiHyQoMHD0bPnj3Rr18/xcxJt6XoQu0MlUqFWbNmYdOmTRgxYgQAWKZDXnvtNVy7dk3mDInI1/l8oTaLiorCCy+80G465Nlnn+V0CBHJioW6DU6HEJFoFH3PxJqaGss34ZqaGpfu0zdp0iQkJCRgx44dyM3NxaVLl7B8+XKMGDECM2fOlCQ/V+MAZdxrEFDGOLz5s9GSt4+jpqYGgOn+h44+57aO5+fnx3smyhUXFhZmaWYJCwtz+T59ERERWLVqFfLz87F582aUlpbi9OnTOHv2LObMmdOqWcad43A1TsT3oiOxoo+DcWLEhYWFATCtNznzORd1HPbiOPXhBE6HEJGcWKidxN0hRCQXFmoXcXcIEXkaC3UHcTqEiDyFhboTWk6HJCaaLmTecjrE267zS0RiYqGWAK8dQkTuxEItIU6HEJE7sFBLjLtDiEhq7Ex0U36BgYF45pln8O2332Lr1q0oKyvDiRMnkJubi2nTpkGr1VqaZUTrTHwn+x3U6eswffh0hPiHdPp41rAzUYw4wPvHwc5EiNWd42pcZzsTpYhLSkrCqFGjkJqair1796KhoQGpqanIysrC4sWLERcXJ/l5O3OsT85/giPfHIHRaMTZy2dx/6D7Mf/e+ZLl5kqsiD9TjBMvjp2JJAlv2R1S21CLt0+8jWZjMxqbG3G97jr25u/Fwh0L8eWPX8qdHpHPYqH2INF3h7yX+x5qdDVoam7CpKGT0CeyDxqbGnG58jKW71+O1z56DVeqr8iaI5EvYqGWgYi7Q0quluDAmQPQN+sxuNdgzLlnDl595FXMiJuBwIBANDY1IuvbLPxu9+/wXs57suRI5KuELNS+cINZ0XaHvH3ibRgMBhiMBsxJnGN5fPzt47HusXUYPXC0ZTpkV84uTocQeZBwdyF/8803cfDgQZvPL1myBI888ogHM3Iv87VDLly4YLmUanZ2Nk6fPo2ZM2c6dSnVzvrk/Cco+LEAeoMek4ZOQr/u/Vo9H6IOwYKxCzBmwBikZKfgUsUly3RI4m2JWDB2AYIQ5NYciXyZcIUaAEaMGIGVK1dCo9HInYrHmKdDWu4O2blzJ44dO9Zqd4jUWi4gBgcGY1rsNJuxg3sPxquPvIojhUewP38/dHodsr7Nwrn/nHNpdwgRuUbIqQ9f5Wh3iDP7XV3VcgFxbuJchKgd75t+4M4H2k2HcHcIkfuwUAvI1u6QN954Q9LdIW0XEMcMHOP0a83TIS9Nfom7Q4jcTJjOxODgYKjVaofHMBgM0Ol00Ov1QncmShEXHR2NNWvWIC0tDR988AH0ej22bduG9PR0zJ8/H8OGDevUOTdkbEBDYwP0zXpMHToV1dXV7eLq6ursHudXob/Cnyb8CYcKDuFo0VHUNtYi8+tM5H+Xj8lDJ2N67HSrr/O298Iab+/oM/P2cbAzEfJ05+Tm5kKr1bZ7PDw8HK+//jqio6OdOp4InYlSxM2bNw9TpkzByy+/jNLSUlRUVGDt2rVITEzEokWLEBUV5fI5M4szUXStCPAHHo55GHf2u9NmbHh4uMPjPXTXQ9CO0GJXzi6cKDqB2qZa7C/Yjy8ufoG/PPIX3BR+k8s5ivheME68OF/oTORiopeIiorC3LlzERYW1undIbUNtXgn+x2nFhBdYW13SGlVKT45/wlm3zNbknMQ+SLOUXsZKZpl3st9Dzcab7i0gOiKwb0Hw8/PD/7+/ugS1AUThkyQ9PhEvoaF2gvZ2x3yxhtv2G2WMS8gNjU3ubyA6KwjhUfwQ/kPUPmrMHX41HbTHkTkGkUX6nfffRc5OTn4+uuvsXPnTrnTkZy13SG5ubntbrS7detWPPzww5g0aRLm/b95VjsQpVLXWIcP8j9AQEAAeob35JQHkQSEnKPuLIPBgPj4eOj1evTu3RsA8NFHHyErKwvHjx+Hn5+fzBlKq2WzzK5du1o1y1y5cgUlJSUAALVajdofapGVmoU/7/5zuw5EKezK2YV6fT3UKjWW3r9U8uMT+SIhC7WtXR+AcwuNd999N5qbmy1F2uyHH37AxIkTcezYMUnzFYF5OiQhIQG7d+9GdnY2jhw5Aj8/PwwYMMAS17VrV4SHh+OtxW9hYdFCSXP4+qevcaLoBNQBatzT/x7E3Bwj6fGJfJVwhXrp0qVYurTj38SOHTuGmpoa9OvX/tviLbfcgm+//Ravvvpqq+JlVl9fj+DgYIfnkCvu/PnzuHz5ssNj9e/fH9XV1fj3v/9tmcNuKTw8HJGRkXh/1/t4bM5jDs/rrF05uxDgH4AwTRgWJkn7jwCRLxOuUANAc3MzAgICOvTa8+fPt9q43taVK1ewfv16jBw5st1zer0egYGBDs8hV1x5eTnOnDnj1LHKysoQGRlpM66qsgr/+9r/SlaoP/3mU/xQ/gPUKjUXEIkkJkxnYtu40NDQDh0vLCwMzc3NNl8TFBSE3r17Q6/Xt3vO3utEiANgNW9rx1Kr1bh+/brNuKCgIMSNjbPajdiSo85EAKhvrMeBMwdghBFdNV0xefBkhz837EwUIw7w/nGwMxFidec4Ezdz5ky88sorVmP1ej2CgoJw5swZ+Pu33/BSVVXl1HnlisvMzMS4ceOcPtY999xjc1rlWvk1fHbqM/xl81+w4vkVCAsJs3lMR52Je07sQaOxEaGaUPxp8p8k6zoU5WeKcWLH+UJnouK254WGhmLfvn34+uuv0djYaHm8oaEBxcXFyMjIsFqklWj37t04f/58q3/Nm5qakH86HyG9Q6BSqXD4w8N4YMYDeDft3Q6dw7yAqPJXcQGRyE0UWbFiY2Oxd+9eXL9+HSdOnMDx48dRXV2Njz/+GLfffrvc6XlMeno6EhISUFJSgoyMDOTl5eH777/HPzb/A/ve34fBwwfD388f9VX1WLtmLWYsmoGz35516RyWBcQgLiASuYsiCzUAJCYmIiUlBUlJSbjrrrvw7rvvYujQoXKn5THFxcX4+OOPERQUhAULFmDChAmIjY3F+vXrMWPGDAwfMBwZOzOQnJyMsK5h8Pf3x7eF32Le/HlY9voy1NTVODxHyw7EyUMncwGRyE0UW6jNNBqNU5dPVRKj0Yi///3vAIDAwEAsWLAAarUaXbp0adfss3j6Ypw6fArTZk5DQGAA0AynpkPadiDaupwpEXWe4gu1Lzpy5Ai+//57AMCMGTPQvXt3u/ERoRHY/OfNSNud1m465KnfP2V1OsTcgajyV7EDkcjNWKgVpra2Ftu3bwdguhbIjBkznH5t/O3x7aZDSs6XtJsO4QIikWexUCvMrl27LLs8Fi9e7FQjTVstp0NUKlW76RB2IBJ5Fgu1ghQXF+PTTz8FAMTHx2PEiBEdPpZ5OmT31t3tpkMy92TCUG9gByKRh6gyMzPtBjh6XmQlJSUoLy8HAOTl5aGiokLmjDrP1vthXkCsqqqCSqVCbGysJbaurs7y93Du3DlLg4CzVi1chQNfHMDu/9uN+pp6XPv2Gmp+qEFRYxE+rf20Q+3+3vxzZaaEMQDePw7z1SHLy8s7/DmPjIxEZWWl1Kl1iNX3w2hHRkaGvactKisrhYwrKCgwarVa46hRo4wFBQXC5edqnL3349ChQ0atVmt88MEHjSkpKa2eq66uNmq1WqNWqzWmpaV1OLfKG5XGZ1Y9Y7w14Vbj+AfGG7VarXHhwoXGU6dOOX08R+Owdl4R47z9s2GmhHEUFBQYR40aZdRqtQ4/5yKPw2i0/X5w6kMBamtrsWPHDgBA9+7dMXPmTLecxzwdcvLQSUwYZ7q9lrN3liGijmOhVoDt27dbFhB/85vfdGgB0RXO3lmGiKTBQu3lzB2IADBs2DAkJCR06nhvvvkmli9fDp1O1+65CxcuYPr06cjLywMgzY12icgxFmovZmzTgfjcc895PAfznWXeeOONdjfafe211zgdQiQBFmov9vHHH1s6EB999FHLNIQcunfv3m46JDs7m9MhRBJgofZSLRcQo6KiMGvWLLecx969Ka3hdAiR9FiovVTLBcRFixa5bQExKCjI5deYp0M2bdpkdTrEmTuKENEvhLxnItnXdgHR2g1sO8PeXeBdYd4dkp+fj82bN6O0tNRyd3SdTodHH33U1KJORHYJe89EKeJqamosc6OO7qUmR36uxgFAZWUl1q1bB71ej4CAADz55JOtxmXtWC3/Hmpra1FVVdUuLjg42HI52BEjRmDlypXtpj0uXLiAF198EQBgMBhQX1/f6ri2REdHY82aNUhLS8MHH3wAvV6Pbdu2IT09HfPnz8ewYcPavcYb3gtv/my05O3j4D0TIdZ9w1yNCwsLs3xjc+Zeap7OryNx2dnZuHz5MgIDAzFr1iwMGjTI4bH8/f0tfw+hoaGW5509pzX+/v7tbkDs6Hjz5s3DlClT8PLLL6O0tBQVFRVYu3YtEhMTsWjRIkRFRbl0PMYxDuA9E0kw9fX1rRYQH3vsMbefU+r55KioKMydO5e7Q4hcwELtRQ4fPmz5FWrhwoVu70B0J+4OIXIeC7WXKC4uxsmTJwGYFhBHjhwpc0adZ293CK8dQvQLFmov0LIDMSAgQJYORHfitUOI7OPeKC9w+PBhj3UgLl1q+/6H0dHR2Ldvn9vObZ4OSU1Nxa5duyzTIceOHcPixYsRFxfntnMTiYzfqAVXW1uLd955B4BpNdhdHYii4LVDiNpjoRbctm3bLAuIDz/8cIc6Bb0Rrx1C9AsWaoEVFxfjyJEjAEwLiEOHDpU5I8/j7hAidibKmp+9OKPR2K4D8aeffurQGJzpTHTleJ2JM3N1HJMmTUJCQgJ27NiB3NxcXLp0CcuXL8fw4cOxcOFCdO/eXZL8fKmjz8zbx8HORIjVneNqnDd3Jh46dMjSgThjxgwMGjQIP/30U4fG0NnORKnjnI1tGxMREYFVq1a1unbImTNnsGzZMsycOdPhtUNEeW8ZJ20cOxNJFi0XELt27eqRDkRvwukQ8jUs1ALaunVrq0uY+soCoiu4O4R8CQu1YIqLi3H06FEApgXE0aNHy5yR2Lg7hHwBC7VAlN6B6E6cDiElY6EWSMsOxGnTpsl6D0RvxGuHkFKxUAui7QLi448/LnNG3ovXDiGlYaEWBBcQpcfpEFIKFmoBXLhwgQuIbsLdIaQE7EyUMT/AtIC4YcMGm/dAbMtXOxM7G6fRaPDcc89hzJgx2Lp1K8rKynDixAnk5uZi2rRp0Gq1UKlUPtXRZ+bt42BnIsTqznE1zhs6E1t2IE6fPt3qPRBdPa9SOxOliEtKSsKoUaOQmpqKvXv3oqGhAampqcjKysLixYsRHR0t5M8y42xjZyK5VXV1NRcQZcDdIeRtWKhltGPHDsuvRAsWLOACoodxdwh5CxZqmbTsQLz99tsxduxYmTPyXdwdQqJjoZZB2w7ERYsWyZwRcXcIiYyFWgYtOxCnTp2KPn36yJwRmfHaISQiFmoPa7uAOGfOHJkzIms4HUIiYaH2MC4geg97u0NSUlI4HUIew0LtQS0XEIcMGcIFRC9hbXdIYWEhp0PIY9iZ6KH82t4D8de//rUlHym7yNiZ6L646OhorFmzBmlpadi+fTtu3LiBbdu2IT09HfPnz8ewYcNkza8jcYB3f8YBdiYCEKs7x9U4kToT09PTLR2I06ZNwx133OG287Iz0b1x8+bNQ7du3XDu3DlkZ2ejoqICa9euRWJiIhYtWoSoqChZ8/O1OHYmkiSqq6vx7rvvAjAtIM6dO1fmjKizIiIiuDuEPIaF2gNaLiA+/fTTXEBUEO4OIU9goXaztguISUlJMmdEUuO1Q8jdWKjdqGUHor+/P37729/KnBG5E68dQu7CQu1GR48ebdWBePPNN8ucEXkCp0NIaizUblJdXY33338fgGkBcfbs2TJnRJ7Ea4eQlFio3WT79u2WBcT58+cjODhY5oxIDrx2CEmBhdoNiouLcezYMQCmBcRx48bJnBHJjdMh1Bl+GRkZRsdh3qmkpARbtmwBYLquxm233eb2c5oXEEtLS+Hv74+lS5eiR48ebj+vPXV1dVi9ejUAQKvVYuTIkbLm4+uqqqpw8OBBFBYWWh678847MWXKFJeahshEis95ZGQkKisrpU5NOkY7MjIy7D1tUVlZKWRcQUGBUavVGkeNGmUsKCjwyHkPHjxo1Gq1Rq1Wa1y/fn2nj9eSM++HtWNVV1dbckpLS3PpnFLHGY0dH4dIcVJ8Nk6dOmVcuHChUavVGh988EHjjBkzjO+//75Rr9d3Oj9PjkPuuIKCAuOoUaOMWq3W4edc5HEYjbbfD059SKjlJUzDw8Mxc+ZMmTMikXE6hJzFQi2h7du3o76+HoDpVzAuIJIj3B1CzmChlkjbBcR7771X5ozIm3B3CNnDQi0BIzsQSSKcDiFrWKglkJ6ebulAnDJlCjsQqVN47RBqi4W6k9ouIPISpiQVXjuEzFioO2nbtm2WBcSnn36aC4gkOU6HEAt1JxQXF+OTTz4BYFpAvO+++2TOiJSKu0N8G++Z2MHzGu3cA7Ejx3MW75koRhwgz2dDo9Hgueeew5gxY7B161aUlZXhxIkTyM3NxbRp06DVaqFSqYQfB++ZaBvvmSjhffo+++wzyz0QtVptu3sguno83jPR/edVUlxSUhJGjRqF1NRU7N27Fw0NDUhNTUVWVhYWL16M6OhorxiHFHG8ZyJZ1XYB8YknnpA5I/JF3B3iO1ioOyAlJcWygMhLmJLcuDtE+VioXVRcXIzjx48DAAYOHIjx48fLnBGRCXeHKBcLtQvMHYhGo5EdiCQk7g5RJhZqF7TsQJw8eTJuvfVWmTMiso7XDlEWFmontV1AfPLJJ2XOiMgxTocoAwu1k1p2IM6dO5cLiOQ17O0OSUlJ4XSIF2ChdkLLDsSBAwfyHojklaztDiksLOR0iBdgZ6KD4xkMBksHop+fH+bNmydc15KjY7EzUTmdiVLERUdHY82aNUhLS8P27dtx48YNbNu2Denp6Zg/fz6GDRsma36uxrEzEWJ157gaJ0Vn4kcffWTpQHz44YcRExODqqoqIcdrK4adiYyzZt68eejWrRvOnTuH7OxsVFRUYO3atUhMTMSiRYsQFRUla37OxrEz0ce1XUB86qmnZM6ISFoRERHcHeIFWKjtaLmAOG/ePC4gkmJxd4jYWKhtaLuAeP/998ucEZF78doh4mKhtsJgMFjugQiAHYjkU3jtEPGwUFvBDkQiZU6H+Pt7Z8lTyZ2Au12vu45rddeQ/mU6ztWfsxtbV1cHGIEtb25Bo64RwV2CETQkCO/lvtcurn+v/rin/z0IDQp1Z/pEsjJPhyQkJOC9995DTk6OZTpk5MiRWLhwYbvdISIz7xDxNoou1BW1FSguK0ZjYyPSv0xHeHm43Xh9kx4/fvYjrpWa5uJuvetWpBakWo1TB6qxdMJSTBgywS25E4mke/fuWL58OfLz87F582aUlpbiiy++QH5+PmbOnIlHH33UsgVURJWVwEsvAf/5zy+PLVwIaLXy5eQKIX8PkGp3RfmNcgCAAQbom/VobG60+19VaRWufHMFBqMBmigNIgZGWI3TN+thNBpxpeaKJHmKrEuXLnKnQAKJi4vDhg0bvGo6JC0NeOopU2E+cMD03zvvAOnpwKpVgE4nd4aOCdeZqNFooFarsXEjcPhw++f79AHWrAEiIozw8/Nz2IVk7jaaHT8bk0ZPshlrMBiwasUqBPcOhp+fH5avWo6b+95sNXZRyiLom/Soq6vrUBdUR+MA6ToTzXN1b775Jg4ePGj1WH379sW6desQFhaG+vp6GAwGl85rDzsTxYgDOjaOSZMmISEhAdu3b8fJkydx6dIlLF++HLGxsViwYAG6d+8uSX4d7UxUq9XQaDT4/ns/7N4NJCcDcXG/vCYyEnjxRWDFCuDoUWDKFCPq6+uh1+slz8+VOMDLOhMBID4eWLYM0Gh+eSwtDXjuOWD1aj/cemsY/Pz8bL4+NDTU8nywJtju/NTRw0dR9lMZVCoVxk8cjyF3DLEZGxAQgEBVIEJCQoTsgnKmM7GxsdHy/IgRI7By5UpoWv5Ft+HM3B47E30rLiIiAq+88gry8/OxceNGXLlyBadPn8ayZcucmg7xRGfioUPAoEGA+ZamjY2NUKvVAIDevU2FesgQAPBDSEiIW/KTIk7IqQ97tFpg9GjTry4NDbaLtCtqqmuw7/19AICQ0BDMfHymJMdVgpbXPyCyJi4uDps2bRJuOkSnA65eNX2TNn8HMTewAabHhtj+PiYUryvUAPDQQ0BREfDVV9Icb3fKbssb+PjcxxESGuLgFb5D5w0TeCS7wMBAy51l7rnnHgC/NMusWbNGlmYZnQ4oLfX4aUUsWHoAAAiuSURBVN3CKwt1165AeHjrFdyOKrlQgs+Pfw4AuLX/rRg3npcwbYnfqMkV5t0hycnJuOmmmwAAX3zxBZtlOskrC7VGA/zcMNUpBoMBW/+5FUajaWHyid880fmDKkxQUJDcKZAXEmE6RKo6IQKvLNRSOfbxMVy6eAkAcO+Ee23u8lC63NxcaLVaTJw40fLf9OnTceHCBbuLtUT2mKdDNm3a1G465K9//avbp0M0GqBHDyA//5cteG07Ezdu9I4teuLuULdDirmnmuoapO4xNbOEhIZg1uxZaDY0S5Cd97G360On09ndDULkSFRUlKVZxrw7JCcnB4WFhW5vlnnoIdPOjq++Mi0qtuwL+O474PPPgccfb72zTERe+Y36+nXT/4cO7fgxuIDonIaGBrlTIIWQYzqkf39TIU5ONn2zNv+GWFkJvP66aevexIluObWkvPIb9aFDprmn3r079vrib4otC4i3Rd+GpPuSJMyOiGwxT4d48tohWq3pS92KFcDPvTEAvKuFXLjOxODgYMuGdGvS0ky/rqxeDQQFGdHYqG+1N7Lt+cy7Fup19aipqYHBYMDmtzZb7oE4a+4s3LhxA8DPF2VyQnNzs9d3JqpUqnZ/z3q9vt3fAe+ZaJsvdyZ2Nk6j0eD555/H2LFjsWXLFly9ehXHjx9HTk4Opk2bBq1WC5VK1el7JqrVagQFBaF/f3+kpLR/rdFoRENDAxobG3nPxI7EAcCpU8CsWa0f69MH2LDB1ALa1NQMtVpts7Bb60w8cugIrl29BpVKhXsn3NuuA9GZDjyldSaaBQYGWj0+75nIOHfFJSUlYeTIkdi/fz/27t2LhoYGpKamIisrC4sXL0Z0dLSk90w0GAytFhT9/Pyg0WisrsOI9Pcn5NSHwWDAkiX+WLLEflx9fb1Lly1su4D42JzHOpOmV2tqaoJarcbSpUvlToV8nHk6ZPz48fjHP/7RajokLi4Ozz//vGTTITU1NS59oRCFkIuJznbD2btIkDUtFxBnzZ7l0wuI5ovPEInCvDukZbNMTk4Om2UgaKGWqohcKLqAuoo6NFY2Iu/zPMsCYt9+fXHvhHslOQcRScvV3SGFhYUoLS3FxYsXUVhYKEPG7ifk1Edn1dXVISlpCn78Ty26qmcDKmDPllz4B1xHXMJAzF8036caOb7//nv8+OOP0Ov1OHfuHKZMmSJ3SkR2ObM7JCQkBElJU3D5sg6BgfejshL4wx/+jrfe2oHjxz/y2ttuWaO4Ql1XV4eYmIfQs2cyRtx9X6vnrlw5jHMFL+GWfrfIlJ3n7du3D8nJybh27RqCg4OxdetW5OTkYPv27XKnRuRQyzvLmJtlvvjiC+Tm5uLkycu45Zb/RkJC+8/50KHjUVBwTOi7zrhCOf/k/CwpaQp69kxGVNR97Z676aYH0bvXi/jN7N/JkJnnpaSk4I9//CN69eqFoUOHIjo6Gv369cOZM2d4Z3XyKm2nQ06cKMAtt/y3zc95cPAzmDr1KRkydQ9l/HPzs7y8PJSVNSI2tv2bZ9anz2zkn/4X3t75Nn7V91etnquvr3fqNmA3Sm+gObAZly5cwpfBX9qOu3HDqVtZORtXUlKCbt26OXUsnU6HV199FQMGDGgXM2DAAGRlZWHjxo0YO3asJLk5Gwe4Ng6pzivHeyFnfkodx5AhQ/DAAw/g3//+zmqRNuvTZzYKC9/B+fPnMcRbLjpth6IKdX5+Pvz973QYV3ujDqtXrkb4r1rf7NZ8FT1HjEYjAvwDUPNZDT7r+pnNOL1ej8DAQIfHczauvLwc+/fvd+pYFRUVKCsrQ9++fa3G1dfXY+XKlRg9erQkuTkbB7g2DqnOK8d7IWd+Sh7HxYsXERqa6PC1FRXX8dZbb2HDhg0OY0WnyszMtBvg6HmRFBUVORlphNFo7NR2n+bmZuh1epSXl3f4GB3h7Pmqq6sdbl9samryeP5mcp1XSkoYA+B94zB3EjtmRGlpqVM1LDIyEpWVlZ1LTCLW8lWNG2f7QvmZmZmw97xZVVWVU5vI3R3XpUsX7Nnze4evC48IRfKfX0ffW1p/26ytrUVoaKjD19fW1uKWnregW6hnf33Py8tDQkKCU8fS6XR48sknbcZpNBqsWLECY8aMkSQ3V6Y+XBmHVOeV472QMz8lj+Orr77CCy+sd/jaHj26YfXq1a2mPkSpVbbYqrmKmvqIj49Hr15BuHr1GHr0uN9qzI8/7sRdMX2wdH77jjzR38SKigrExMQ4faxVq1Zh2bJlGDhwYKuY4uJi3HfffXj22Wcly83ZOMD1cYgY58wY5MxPyeOIiYnBunVbHH7Ob789ShHz04DCCjUAZGYewPDhDwEwokeP1tcvLCs7CJ1uCz788FN5kvOwxx57DGq1Gv/1X/+FmpoaywVq7r77bvztb3+TOz2iDvO1z7niCnVwcDDOnj2M8eOn4tSpP0OlMn1baG4uxIAB3ZCTkyFzhp71yCOPICEhAcePH0dlZSWGDx+O0aNHO3XFNCJR+drnXHGFGjDNv2ZlHcHp06eRl5eHoqIizJnzFmJjY+VOTRZ9+/bF3Llz5U6DSFItP+e7du3CoEGDkJDwrCI/54os1GaxsbGIjY1FZmamIt88IjJ9zqurq53a+OCtFNeZSESkNCzURESCY6EmIhKccPdMdEcc4Dvj8IYxAMoYh6/8TLnjvKKNw8/Pj/dMZJxn40TOzZVY0cfBOMZ5Ko5TH0REgmOhJiISHAs1EZHgWKiJiATHQk1EJDgWaiIiwbFQExEJjoWaiEhw7Ex043nZmWibEsbhKz9T7jivaONgZyLjPB4ncm6uxIo+DsYxzlNxnPogIhIcCzURkeBYqImIBMdCTUQkOBZqIiLBsVATEQmOhZqISHAs1EREgmNnohvPy85E25QwDl/5mXLHeUUbBzsTGefxOJFzcyVW9HEwjnGeiuPUBxGR4FioiYgEx0JNRCS4/w/egRT3bjr5IQAAAABJRU5ErkJggg==)