Question

two circles inersect each other at point A and D diameters of circles are two sides of triangle prove that point of intersection of two circles lies on the third side of circle​

Answer 1

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.

hope it helps u

Answer 2

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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.