Question

# Two equal circles of radius $$R$$ are touching each other externally. If a smaller circle of radius $$r$$ is touching both of these circles as well as their direct common tangent, then the ratio $$r : R$$ is

A
1:2
B
1:2
C
1:22
D
1:4

Solution

## The correct option is D $$1 : 4$$Length of common tangent to circles of equal radii = $$2 \times radius$$ Here $$l = 2R$$ $$\implies AD = DC = BE = \dfrac{1}{2} = R$$ $$AB = R + r$$ $$AE = R - r$$ $$AB^2 = AE^2 + BE^2$$ $$\implies (R + r)^2 = (R - r)^2 + R^2$$ $$\implies 4Rr = R^2$$ $$\implies \dfrac{4}{1} = \dfrac{R}{r} \implies r:R = 1:4$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More