Question

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? ​

Answer 1

Answer:

Given,

Two circles are drawn on the sides AB and AC of the triangle

ABC as diameters. The circles intersected at D.

Construction: AD is joined.

To prove: D lies on BC. We have to prove that BDC is a straight line.

Proof:

∠ADB=∠ADC=90° ...Angle in the semi circle

Now,

∠ADB+∠ADC=180°

⇒∠BDC is straight line.

Thus, D lies on the BC.

solution