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.
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