Question

if circles are drawn taking two sides of a triangle as diameter prove that the point of intersection of the circle lie on the third side​

Answer 1

Data: Two circles are drawn taking PQ and PR of a triangle as diameter.

Let these intersect at P and S.

To Prove: The point of intersection ‘S’ is on the third side QR of ∆PQR.

Construction: Join PS. Proof: QAP is a diameter.

∴ ∠QSP = 90° (angle in the semi circle)

Similarly, ABR is a diameter.

∠PSR – 90° (angle in the semicircle)

∠QSR = ∠QSP + ∠RSP = 90 + 90

∠QSR = 180°

∴ ∠QSR is straight angle.

∴ QSR is a straight line.

∴ Point ‘S’ is on third side QR of ∆PQR.

Once again hope it helps uh parth ❤︎