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17 tháng 1 2023
a: góc KOA+góc BOA=90 độ
góc KAO+góc COA=90 độ
mà góc BOA=góc COA
nên góc KOA=góc KAO
=>ΔKAO cân tại K
b: Xét ΔOBA vuông tại B có sin BAO=OB/OA=1/2
nên góc BAO=30 độ
=>góc BOA=60 độ
Xét ΔOBI có OB=OI và góc BOI=60 độ
nên ΔOBI đều
=>OI=OB=1/2OA=R
=>I là trung điểm của OA
ΔKAO cân tại K
mà KI là trung tuyến
nên KI vuông góc với OI
=>KI là tiếp tuyến của (O)
Lời giải:
a.
$OB=OC$ nên tam giác $OBC$ cân
Do đó đường cao $OH$ đồng thời là trung tuyến hay $H$ là trung điểm $BC$
$\Rightarrow BH=4$ (cm)
Do $BA$ là tiếp tuyến $(O)\Rightarrow BA\perp BO$
Áp dụng HTL trong tam giác vuông với tam giác $ABO$:
$\frac{1}{AB^2}+\frac{1}{BO^2}=\frac{1}{BH^2}$
$\frac{1}{AB^2}+\frac{1}{5^2}=\frac{1}{4^2}$
$\Rightarrow AB=\frac{20}{3}$ (cm)
$AO=\sqrt{AB^2+BO^2}=\sqrt{(\frac{20}{3})^2+5^2}=\frac{25}{3}$ (cm)
b.
Vì $AO$ cắt $BC$ tại trung điểm $H$ của $BC$ và $AO\perp BC$ nên $AO$ là đường trung trực của $BC$
$\Rightarrow AC=AB$. Mà $OB=OC$ nên:
Do đó $\triangle ACO=\triangle ABO$ (c.c.c)
$\Rightarrow \widehat{ACO}=\widehat{ABO}=90^0$
$\Rightarrow AC\perp CO$ nên $AC$ là tiếp tuyến $(O)$
$AC=AB=\frac{20}{3}$ (cm)
Hình vẽ:
![](data:image/png;base64,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)