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Angle Subtended by Diameter on the Circle

The following...

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

Given: $PQ = 7 \ cm, QR = 3RS = 6 \ cm$

$PR = \sqrt{7^2+6^2} = \sqrt{85}$

$SR = \sqrt{PR^2-PS^2} = \sqrt{85-4} =9$

Therefore the perimeter of $PQRS = 2+9+6+7 = 24 \ cm$

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