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)