Consider the circles of radius and of radius both lying the first quadrant and…

MATHEMATICS · Subjective · ICSE · Mathematics · Geometry · Geometry

Problem

Consider the circles

C_1

of radius

a

and

C_2

of radius

b, b > a

both lying the first quadrant and touching the coordinate axes.

Column I	Column II
(A) $C_1$ and $C_2$ touch each other and $\frac{b}{a} = \lambda + \sqrt{\mu}, \lambda \in \text{prime number and } \mu \in \text{whole number, then}$	(p) $\lambda + \mu$ is a prime number
(B) $C_1$ and $C_2$ cut orthogonally and $\frac{b}{a} = \lambda + \sqrt{\mu}, \lambda \in \text{prime number and } \mu \in \text{whole number, then}$	(q) $\lambda + \mu$ is a composite number
(C) $C_1$ and $C_2$ intersect so that the common chord is longest and $\frac{b}{a} = \lambda + \sqrt{\mu}, \lambda \in \text{prime number and } \mu \in \text{whole number, then}$	(r) $2\lambda + \mu$ is a perfect number
(D) $C_2$ passes through the centre of $C_1$ and $\frac{b}{a} = \lambda + \sqrt{\mu}, \lambda \in \text{prime number and } \mu \in \text{whole number, then}$	(s) $\lambda - \mu$ is a prime number