If the two sides of a pair of opposite sides of a cyclic quadrilateral

1.	If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.
Answer» Given that, ABCD is cyclic quadrilateral in which AB = DC To prove : AC = BD Proof : In ΔPAB and ΔPDC, AB = DC (Given) ∠BAP = ∠CDP (Angles in the same segment) ∠PBA = ∠PCD (Angles in the same segment) Then, ΔPAB = ΔPDC ... (i) (By c.p.c.t) PC = PB ... (ii) (By c.p.c.t) Adding (i) and (ii), we get PA + PC = PD + PB AC = BD

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

Answer»

Given that,

ABCD is cyclic quadrilateral in which AB = DC

To prove :

AC = BD

Proof :

In ΔPAB and ΔPDC,

AB = DC (Given)

∠BAP = ∠CDP

(Angles in the same segment)

∠PBA = ∠PCD

(Angles in the same segment)

Then,

ΔPAB = ΔPDC ... (i)

(By c.p.c.t)

PC = PB ... (ii)

(By c.p.c.t)

Adding (i) and (ii), we get

PA + PC = PD + PB

AC = BD

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

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