If the circles are drawn taking two sides of a triangle as diameters ,prove that the point of intersection of these circles lie on the third side.

Asked by bansari Butani | 19th Feb, 2014, 02:14: PM

Expert Answer:

Dear Student,
 
Consider a triangleABC.
Two circles are drawn while taking AB and AC as the diameter.
Let they intersect each other at D and let D not lie on BC.
Join AD
 
∠ADB = 90°           (Angle subtended by semi-circle)
∠ADC = 90°            (Angle subtended by semi-circle)
∠BDC = ∠ADB + ∠ADC = 90° + 90° = 180°
 
Therefore, BDC is a straight line and hence, our assumption was wrong.
Thus, Point D lies on third side BC of ΔABC.
 
 
 
 
Thanks and Regards
Toppers Team
 

Answered by  | 19th Feb, 2014, 06:19: PM

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