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Question

If a pair of opposite sides of a cylic quadrilateral are equal, prove that its diagonals are equal. [3 MARKS]

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Solution

Concept: 1 Mark
Steps: 1 Mark
Answer: 1 Mark

Given: A cyclic quadrilateral ABCD in which AB = DC.

To Prove: Diagonal AC = Diagonal BD.

Proof :

BAC=BDC ..... (i) [Angles in the same segment of a circle. ]

CAD=ADB .....(ii) [ Equal arcs CD and AB subtend equal angles at the circumference ]

BAC+CAD=BDC+ADB [Adding (i) and (ii)]

BAD=ADC

BD=AC [Equal angles on the same circle cut off equal chords.]

diagonal AC=diagonal BD.

Hence Proved.


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