標題:
Geometry : Circle
發問:
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.]
最佳解答:
其他解答:
Geometry : Circle
發問:
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.]
最佳解答:
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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.其他解答:
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