Q22 of 100 Page 17

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

Given that,

ABCD is cyclic quadrilateral in which AB = DC


To prove: AC = BD


Proof: In and ,


AB = DC (Given)


∠BAP = ∠CDP (Angles in the same segment)


∠PBA = ∠PCD (Angles in the same segment)


Then,


(i) (By c.p.c.t)


(ii) (By c.p.c.t)


Adding (i) and (ii), we get


PA + PC = PD + PB


AC = BD


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