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Question
A quadrilateral PQRS circumscribes a circle. If PS + QR = 10 cm, what is the perimeter of the quadrilateral?
A quadrilateral PQRS circumscribes a circle. If PS + QR = 10 cm, what is the perimeter of the quadrilateral?
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Solution
The correct option is B 20 cm
Solution - A, B, C, D are the points where circle touches the quadrilateral.
We know that 2 tangents from an external point to a circle are equal in length
From the figure we can see that
PD = PA = a,
SD = SC = b,
RC = RB = c,
QB = QA = d,
therefore PS + QR + PQ + SR = a + b + c + d + a + d + b + c
= 2(a + b + c + d)
= 2 x 10
= 20cm
20 cm
Solution - A, B, C, D are the points where circle touches the quadrilateral.
We know that 2 tangents from an external point to a circle are equal in length
From the figure we can see that
PD = PA = a,
SD = SC = b,
RC = RB = c,
QB = QA = d,
therefore PS + QR + PQ + SR = a + b + c + d + a + d + b + c
= 2(a + b + c + d)
= 2 x 10
= 20cm
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