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Question

The quadrilateral formed by joining the angle bisectors of a cyclic quadrilateral is a


A

Rectangle

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B

square

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C

parallelogram

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D

cyclic quadrilateral

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Solution

The correct option is D

cyclic quadrilateral


ABCD is a cyclic quadrilateral ∴A +C = 180 and B+ D = 180

12A+12 C = 90 and 12 B+12 D = 90

x + z = 90 and y + w = 90

In ARB and CPD, x+y + ARB = 180 and z+w+ CPD = 180

ARB = 180 – (x+y) and CPD = 180 – (z+w)

ARB+CPD = 360 – (x+y+z+w) = 360 – (90+90)

= 360180 ARB+CPD = 180

SRQ+QPS = 180

The sum of a pair of opposite angles of a quadrilateral PQRS is 180.

Hence PQRS is cyclic


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