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.


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