2 equal chords of a circle intersect within the circle. PT line joining the point of intersection to the centre make equal angles with the chords.

Given, the equal chords AB and AC of a circle C (O, r)

To prove: ∠OAB = ∠OAC

Construction: Join OB and OC.

Proof: In ΔOAB and ΔOAC, we have

AB = AC (Given)

OA = OA (Common)

and OB = OC (Radii of same circle)

⇒ ∠OAB = ∠OAC (c.p.ct)