Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drwan.

Show that the points A, Q and B are collinear.

Dear Student!

Here is the answer to your query.

Given : P and Q are the points of intersection of two circles with diameter PA and PB

To Prove : Points A, Q and B are collinear

Construction : Join PQ

Proof : In ΔPAQ

∠PQA = 90°  (Angle in a semicircle)      ... (1)

In ΔPQB

∠PQB = 90°        (Angle in a semicircle)        ... (2)

adding (1) and (2) we get

∠PQA + ∠PQB = 90° + 90°

⇒∠AQB = 180° 

∴Points A, Q and B are collinear.

Cheers!