Question

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

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

Answer 1

The correct option is C 24 cm

Given: PS = QR = 25 cm, PQ = 18 cm and SR = 32 cm
Draw a perpendicular from P on SR at X, and from Q on SR at Y
thus, $PX=QY=diameter$
Now, In $△PSX$ and $△QRY$
$PS=QR$ (Given)
$\angle PXS=\angle QYR$ (Each 90)
$PX=QY$ (distance between parallel lines)
hence, $△PSX\cong △QRY$ (SAS rule)
thus, $SX=RY=\frac{32-18}{2}=7$
Now, In $△PSX$, Using Pythagoras Theorem,
$P{S}^2=P{X}^2+S{X}^2$
${25}^2=P{X}^2+7^2$
$PX=24$ cm