Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).
Given: In ΔABC, circles are drawn with sides AB and AC as diameter.
To prove: Circles drawn on AB and AC intersect at D which lies on BC, the third side.
Construction: Draw AD ⊥ BC.
Proof : ∵AD⊥BC
So, the circles drawn on sides AB and AC as diameter will pass through D.
Hence, circles drawn on two sides of a triangle pass through D, which lies on the third side.