Question

A circle is centered at origin. 2 points P and Q lies on the positive x axis outside the circle such that OQ = 2OP. The length of tangent drawn from Q to the circle is thrice the length of tangent from P to the circle. What the radius of circle if OP = a.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let's draw the figure of circle and points P and Q as given by the question.

Tangents are drawn from P and Q to the circle, PX and QY.

$P\equiv (a,0)$

$Q\equiv (2a,0)$

Its given that,

$QY=3PX$

While dealing with length of the tangents its better to remember the equation for length of tangent

$i.e.,L=\sqrt{S_1}$

$i.e.,Q=3PX$

$\sqrt{x_1^2+y_1^2-r^2}=3\sqrt{x_2^2+y_2^2-r^2}$

$\sqrt{4a^2+O-r^2}=3\sqrt{a^2+O-r^2}$

Squaring both sides

$4a^2-r^2=9(a^2-r^2)$

$=9a^2-9r^2$

$5a^2=8r^2$

$\therefore r=\sqrt{\frac{5}{8}}a$