JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Properties of Triangle

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

x

-axis at

R

and tangents to the parabola at

P

and

Q

intersect the

x

-axis at

S

.

The radius of the incircle of the triangle

P QR

(A)4
(B)3
(C) $\frac{8}{3}$
(D)2✓ Correct

Answer: (D)

Solution

Points:

P = (1, 22)

Q = (1, - 22)

R = (9, 0)

P Q = 42

P R = QR = (9 - 1)^{2} + (22)^{2} = 64 + 8 = 72 = 62

Semi-perimeter:

s = \frac{4 2 + 6 2 + 6 2}{2} = 82

Area:

Δ = 162

(from previous calculation)

Inradius:

r = \frac{Δ}{s} = \frac{16 2}{8 2} = 2

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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