Question

In the given figure, a circle with centre O has diameter 16 cm. If PQ = 2 cm, then the measure of RS is

• A. $2\sqrt{7}cm$
• B. $2\sqrt{28}cm$
• C. $\sqrt{28}cm$
• D. $4\sqrt{7}cm$

Answer 1

Answer: (B), (D)

The correct options are
B

$2\sqrt{28}cm$

D

$4\sqrt{7}cm$

Given, diameter = 16 cm

$⟹$ OR = OQ = 8 cm

and, OP = OQ - PQ = 8 cm - 2 cm = 6 cm

Using Pythagoras theorem in $△$OPR,

$RP=\sqrt{O{R}^2-O{P}^2}=\sqrt{8^2-6^2}=\sqrt{28}cm=2\sqrt{7}cm$

We know that the perpendicular from th centre to a chord bisects the chord, and hence $RS=4\sqrt{7}cm\text{as}RP=2\sqrt{7}cm$