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Question
The following figure shows a circle with PR as its diameter. If PQ = 7 cm and QR = 3RS = 6 cm, find the perimeter of the cyclic quadrilateral PQRS.
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Solution
In the figure, PQRS is a cyclic quadrilateral in which PR is a diameter
PQ = 7 cm
QR = 3RS = 6 cm
3RS = 6 cm
RS = 2 cm
Now in ∆PQR,
∠Q = 90° ...[Angles in a semi-circle]
∴ PR2 = PQ2 + QR2 ...[Pythagoras theorem]
= 72 + 62
= 49 + 36
= 85
Again in right ΔPSQ,
PR2 = PS2 + RS2
`=>` 85 = PS2 + 22
`=>` PS2 = 85 – 4 = 81 = (9)2
∴ PS = 9 cm
Now, perimeter of quad PQRS
= PQ + QR + RS + SP
= (7 + 9 + 2 + 6) cm
= 24
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