A circle is inscribed in a trapezium PQRS. If PS = 25 cm, PQ = 18 cm and SR = 32 cm, what is the length of the diameter of the circle?

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Solution

The correct option is D 24
Since length of tangents drawn from a particular point to the circle is equal, by solving we get QR is equal to PS.
Hence PQRS is an isosceles trapezium.
Drawing perpendicular from P to SR intersecting at A and Q to SR intersecting at B.
Hence in right angled $Δ$ PSA, PS = 25, SA = 7. Hence PA = 24. Height PA = 24 cm.
Therefore, diameter of circle is 24 cm.

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