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AB and AC are two equal chords of a circle and AP and AQ are two another chords of circle intersects BC in S and and R prove that PQRS is a cyclic



In triangle ABC, since chords AB and AC are equal, EXPERT ANSWER Ruchira Banka , Meritnation Expert added an answer 24 helpful votes in Math ∠ABC = ∠ACB......(i) 

Also, 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

∠ABC = ∠AQC (angles in the ∠ACB = ∠AQC ∠APQ + ∠ACQ = 180° ∠APQ + ∠ACB + ∠BCQ = 180 ∠APQ + ∠AQC + ∠BCQ = 180 ∠BCQ + ∠AQC = SRQ....(iv) ∠APQ + ∠SRQ = 180° 


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