JEE Main · 2014 · 06 Apr 2014 · Offline · Circle

Let C be the circle with centre at

(1, 1)

and radius

= 1

. If T is the circle centred at

(0, y)

, passing through origin and touching the circle C externally, then the radius of T is equal to

(A) $\frac{3}{2}$
(B) $\frac{3}{2}$
(C) $\frac{1}{2}$
(D) $\frac{1}{4}$ ✓ Correct

Answer: (D)

Solution

Circle

C

is centred at

(1, 1)

with radius

1

, and circle

T

is centred at

(0, y)

and passes through the origin, so its radius is

y

. For the two to touch externally the distance between centres must equal the sum of the radii:

1 + (1 - y)^{2} = 1 + y

. Squaring,

1 + 1 - 2 y + y^{2} = 1 + 2 y + y^{2}

, which reduces to

2 - 2 y = 1 + 2 y

, so

4 y = 1

and

y = \frac{1}{4}

. That is the radius of

T

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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