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Question: C<sub>1</sub> is a circle of radius 2 touching the x-axis and the y-axis. C<sub>2</sub> is another c...

C1 is a circle of radius 2 touching the x-axis and the y-axis. C2 is another circle of radius > 2 and touching the axes as well as the circle C1. Then the radius of C2 is-

A

6 – 424 \sqrt { 2 }

B

6 + 424 \sqrt { 2 }

C

6 –434 \sqrt { 3 }

D

6 +434 \sqrt { 3 }

Answer

6 + 424 \sqrt { 2 }

Explanation

Solution

C1 (2, 2) r1 = 2

C2 (r, r) r2 = r

and C1C2 = r1 + r2

(r –2)2 + (r –2)2 = (2 + r)2

r2 – 12r + 4 = 0

r = 6 ±424 \sqrt { 2 }

6 –424 \sqrt { 2 }< 2 then r = 6 +424 \sqrt { 2 }