Question

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

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

Answer 1

The correct option is C $24cm$

Given : $PS=QR=25cm,PQ=18cmandSR=32cm$

Drawing perpendicular from P and Q to meet SR at X and Y respectively.

Let AB be the diameter of the circle, where AB=PX

We see that $XY=PQ=18cm$

Also $SX=YR$ which gives us $SX=YR=\frac{32-18}{2}=7cm$

By applying the pythagorean theorem in $△PXS$, we get

$P{X}^2+7^2={25}^2$

$P{X}^2=576$

$PX=24cm$

As $PX=AB$

And AB is the diameter of the circle, therefore the diameter of the circle is$24cm$