Abcd Is Cyclic Quadrilateral Ab And Dc Are Produced To Meet In E

ABCD is a cyclic quadrilateral AB and DC are produced to meet in E. Prove that ΔEBC ~ ΔEDA.


In triangle EBC and EDA, we have

∠EBC = ∠EDA    [∵   Exterior angle in a cyclic quad.  is equal to opposite interior angle]

∠ECB = ∠EAD    [∵  Exterior angle in a cyclic quad. is equal to opposite interior angle ]

and     ∠E = ∠E

so, by AAA interior of similarity, we get


Hence proved.