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1) Xét (O) có
DC là tiếp tuyến có C là tiếp điểm
DA là tiếp tuyến có A là tiếp điểm
Do đó: DC=DA
Xét (O) có
EC là tiếp tuyến có C là tiếp điểm
EB là tiếp tuyến có B là tiếp điểm
Do đó: EC=EB
Ta có: DE=DC+CE(C nằm giữa D và E)
nên DE=DA+EB(đpcm)
Tự ngắt dòng | |
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...
HP
17 tháng 12 2020
Hình vẽ: a, \(AH\perp MC\Rightarrow AH=HD\) Ta có \(\left\{{}\begin{matrix}OA=OD\\HA=HD\end{matrix}\right.\Rightarrow OM\) là trung trực của \(AD\) \(\Rightarrow MA=MD\Rightarrow\Delta OAM=\Delta ODM\left(c-c-c\right)\) \(\Rightarrow MD\perp OD\) Hay MD là tiếp tuyến b, \(\Delta OAM\) vuông tại A \(\Rightarrow O;A;M\) thuộc đường tròn đường kính OM Lại có \(\Delta ODM\) vuông tại D \(\Rightarrow O;D;M\) thuộc đường tròn đường kính OM Dễ chứng minh được B là trung điểm OM \(\Rightarrow M;A;O;D\in\left(B;R\right)\) c, Vì \(\widehat{BAC}=90^o\Rightarrow\Delta BAC\) vuông tại A \(\Rightarrow HB.HC=HA^2\) Mà \(\Delta OAM\) vuông tại A \(\Rightarrow HM.HO=HA^2\) \(\Rightarrow HB.HC=HM.HO\) 28 tháng 7 2021
1) Xét (O) có DA là tiếp tuyến có A là tiếp điểm DC là tiếp tuyến có C là tiếp điểm Do đó: DA=DC Xét (O) có EC là tiếp tuyến có C là tiếp điểm EB là tiếp tuyến có B là tiếp điểm Do đó: EC=EB Ta có: DE=DC+CE nên DE=DA+EB |