AB and AC are two equal chords of a circle and AP, AQ are two other chords which intersect BC in S and R respectively. Prove that PQRS is a cyclic quadrilateral.
To prove PQRS is cyclic, it suffices to prove that a pair of opposite angles is supplementary.Join BC, BP and CQ as shown
In triangle ABC, since chords AB and AC are equal,
From (i) and (ii)
Since APQC is a cyclic quadrilateral,
Now , exterior angle in a triangle is equal to sum of interior opposite angles.
Using (iv) in (iii);
These are opposite angles of quadrilateral PQRS. So, PQRS is a cyclic quadrilateral