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Question

Question 10
If 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.


Solution


Consider a ΔABC.
Two circles are drawn while taking AB and AC as the diameter.
Let they intersect each other at D.
Assume that the point of intersection 'D' doesn't lie on BC and 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.

 


Mathematics
DUMMY
Standard IX

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