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JEE Advanced 2007Paper 1

Exam: JEE Advanced
Year: 2007
Paper: Paper 1
Subject: Mathematics
Chapter: Properties of Triangles

JEE Advanced 2007 · Paper 1 · Mathematics · Properties of Triangles

Paragraph: Consider the circle x^2+y^2=9 and the parabola y^2=8 x ....

Paragraph: Consider the circle

x^2+y^2=9

and the parabola

y^2=8 x

. They intersect at

P

and

Q

in the first and the fourth quadrants, respectively. Tangents to the circle at

P

and

Q

intersect the

\mathrm{X}

-axis at

R

and tangents to the parabola at

P

and

Q

intersect the

\mathrm{X}

-axis at

S

.Question: The radius of the incircle of the

\triangle P Q R

is

Options

A4
B3
C $\frac{8}{3}$
D2

Correct answer

D. 2

Step-by-step solution

Radius of incircle is,

r=\frac{\Delta}{s}

As

\Delta=16 \sqrt{2}

\begin{aligned}& \therefore \quad s=\frac{6 \sqrt{2}+6 \sqrt{2}+4 \sqrt{2}}{2}=8 \sqrt{2}\\ & \therefore \quad r=\frac{16 \sqrt{2}}{8 \sqrt{2}}=2 \\ & \end{aligned}

$

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