In the given figure, chords and of a circle are produced to meet at Prove that and are similar.

If one side of a cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

Chord AB of a circle is produced to E.

∴ ext. ∠BDE = ∠BAC = ∠EAC ___________________ (i)

Chord CD of a circle is produced to E.

∴ ext. ∠DBE = ∠ACD = ∠ACE ____________________ (ii)

In ΔEDB and ΔEAC,

∠BDE = ∠CAE [From equation (i)]

∠DBE = ∠ACE [From equation (ii)]

∠E = ∠E [Common angle]

∴ ΔEDB ∼ ΔEAC Proved.