Question

If $PS=QR=25cm,PQ=18cm$ and $SR=32cm$, in the given figure 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 $24cm$

Let $PA$ and $QB$ be perpendicular lines to $SR$
$⟹SR=SA+RB+PQ$

$⟹SA+RB=32–18=14⟹SA=14-RB$

$PA=QB=diameter$

In $△PSA$

$P{S}^2=(SA{)}^2–d^2$

$⟹P{S}^2–d^2=S{A}^2–eq.1$

In $△QRB$

$Q{R}^2–d^2=R{B}^2–eq.2$

From eq.1 and eq.2

$SA=RB=\frac{1}{2}\times 14=7cm$

$d^2=Q{R}^2–R{B}^2$

$d=\sqrt{{25}^2–7^2}=\sqrt{576}=24$