#### Question

Two circles intersect at P and Q. through P diameter PA and PB of the two circles are drawn.

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

#### Solution

Let O and O' be the centres of two intersecting circle, where

Points of intersection are P and Q and PA and PB are their diameter respectively.

Join PQ, AQ and QB.

∴ ∠AQP = 90° and ∠BQP = 90°

(Angle in a semicircle is a right angle)

Adding both these angles,

∠AQP + ∠BQP = 180° ⇒ ∠AQB = 180°

Hence, the points A, Q and B are collinear.

Is there an error in this question or solution?

Solution Two Circles Intersect at P and Q. Through P Diameter Pa and Pb of the Two Circles Are Drawn. Show that the Points A, Q and B Are Collinear. Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.