Question

A circle is inscribed in trapezoid $PQRS$. If $PS=QR=25cm,PQ=18cmandSR=32cm$, what is the length of the diameter of the circle ?

• A. $14cm$
• B. $25cm$
• C. $24cm$
• D. $\sqrt{674}cm$

Answer 1

Answer: (C)

$24cm$

Given:PQRS is a Trapezoid.

PQ=QR=25cm

SR=32cm

PQ=18cm

Draw perpendiculars from P and Q to meet SR at X and Y respectively.

AB is diameter of circle

PX=AB

Also ,PQ=XY

XY=18.....(1)

Also SX = YR

SX = YR =half of (SR-XY)=7cm

SX=7cm...(2)

$InRightangle△PXS{PS}^2={SX}^2+{PX}^2{25}^2=7^2+{PX}^2\left[From\right(2\left)\right]\Rightarrow {PX}^2=625-49\Rightarrow {PX}^2=576\Rightarrow PX=24$

Since PX=AB

AB=24cm id diameter of cicle.

Hence option (C) is the correct answer.