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Question
In the figure alongside PR is a diameter of the circle, PQ = 7 cm; QR = 6 cm and RS = 2 cm. Calculate the perimeter of the cyclic quadrilateral PQRS.
Solution
PR is the diameter of the circle.
then ∠ PQR = 90° .....(Angle in semicircle)
In Δ PQR,
PR = `sqrt((7)^2 + (6)^2)`
PR = `sqrt(49 + 36)`
PR = `sqrt(85)`
Similarly,
∠ PSR = 90°
In ΔPSR,
PS = `sqrt("PR"^2 - "SR"^2)`
PS = `sqrt(85 - 4)`
PS = `sqrt(81)`
PS = 9 cm
Perimeter of cyclic quadrilateral PQRS = PQ + QR + RS + PS
Perimeter of cyclic quadrilateral PQRS = 7 cm + 6 cm + 2 cm + 9 cm = 24 cm
Perimeter of cyclic quadrilateral PQRS = 24 cm.
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