Question

Consider the circle $x^2+y^2=9$ and the parabola $y^2=8x$. They intersect at $P$ and $Q$ in the first and fourth quadrants, respectively. Tangents to the circle at $P$ and $Q$ intersect the $x$-axis at $R$ and tangent to the parabola at $P$ and $Q$ intersect the $x$-axis at $S$.
The radius of the incircle of the triangle $PQR$ is -

• A. $4$
• B. $3$
• C. $\frac{8}{3}$
• D. $2$

Answer 1

The correct option is D $2$

Radius of incircle is $r=\frac{\Delta }{s}$

as $\Delta =16\sqrt{2}$

$s=\frac{(6\sqrt{2}+6\sqrt{2}+4\sqrt{2})}{2}=8\sqrt{2}$

$r=\frac{16\sqrt{2}}{8\sqrt{2}}=2$