Question
Question: Three equal circles each of radius r touch one another. The radius of the circle touching all the th...
Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is –
A
(2 +3 ) r
B
3(2+3)r
C
3(2–3)r
D
(2 – 3) r
Answer
3(2+3)r
Explanation
Solution
Q DDEF is equilateral with side 2r if radius of circum circle DEF is R1, then
Area of DDEF =43 (2r)2 = 3r2
3r2 = 4R12r.2r.2r Ž R1 = 32r
\ Radius of the circle touching all the three given circles
= r + R1
= r + 32r= 3(2+3)r