Question

The length of a tangent extended from a point P situated outside a circle is $\sqrt{5}$ units. Another line from P intersects the circle at 2 points R and S such that PR: RS = 1: 2. What is the length of PS?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given that

$\frac{PR}{RS}=\frac{1}{2}$

By power of a point theorem

$P{Q}^2=PR\times PS$

$i.e.,PR\times (PR+RS)=5$

(Since $PS=PR+PSandP{Q}^2=5$)

$\frac{RS}{2}\times [\frac{RS}{2}+RS]=5$

$R{S}^2.\frac{3}{4}=5$

$RS=2\sqrt[2]{2\frac{5}{3}}$

$PR=\sqrt{\frac{5}{3}}$

$\therefore PS=PR+RS=3\sqrt[2]{2\frac{5}{3}}$

$=\sqrt{3\times 5}$

$=\sqrt{15}$