Geometry : Circle
2011-10-22 3:12 am
A and B are 2 circles with different radius that intersects at 2 point X and Y. PQ is a common tangent of the 2 circles that touches the circles at P and Q respectively. Chord XY produces and cut the common tangent PQ at point M, prove that PM = MQ. [ Prove by co - ordinate geometry not acceptable.]
回答 (1)
2011-10-22 5:31 pm
✔ 最佳答案
圖片參考：http://imgcld.yimg.com/8/n/HA04628698/o/701110210062313873483000.jpg
ㄥPXY = ㄥYPM (∠in alt. segment)
ㄥXMP = ㄥPMY (common)
∴ △XMP ~ △PMY (A.A.)
Therefore
MP : MY = MX : MP
MP² = MY * MX
Similarly ,
MQ² = MY * MX
Hence MP² = MQ²
MP = MQ
Q.E.D.
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111021000051KK00623