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.
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≡(a,0)
Q≡(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=√S1
i.e.,Q=3PX
√x21+y21−r2=3√x22+y22−r2
√4a2+O−r2=3√a2+O−r2
Squaring both sides
4a2−r2=9(a2−r2)
=9a2−9r2
5a2=8r2
∴r=√58a