Question

$PQ$ is the diametre of a semicircle with radius $4cm$ and $\angle PRQ$ is the angle on the semicircle. If $QR=2\sqrt{7}cm$, then length of $PR$ is

• A. $8cm$
• B. $6cm$
• C. $5cm$
• D. $2\sqrt{11}cm$

Answer 1

Answer: (B)

$6cm$

Given that,

$QR=2\sqrt{7}cm$

$OQ=4cm\left[radius\right]$

$PQ=2\times 4=8cm\left(diametre\right)$

In $\Delta PQR$

$PR=\sqrt{P{Q}^2-Q{R}^2}$

$=\sqrt{8^2-{\left(2\sqrt{7}\right)}^2}$

$=\sqrt{64-28}$

$=\sqrt{36}$

$=6$ cm

Required length of $PR=6cm$