Question

Two spheres of radii 3 and 4 cut orthogonally The radius of common circle is

• A. $12$
• B. $\frac{12}{5}$
• C. $\frac{\sqrt{12}}{5}$
• D. $\sqrt{12}$

Answer 1

Answer: (B)

$\frac{12}{5}$

Answer 2

For the orthogonal section $C_1P$ and $C_2P$ are pendicular where $C_1$ and $C_2$ are centres of sphere of radii $4$ and $3$ respectively Now $C_1P = 4$ and $C_2P = 3$, so $tan\,\theta = \frac{3}{4}$ $\therefore$ Radius of circle of intersection $OP = C_{1}P \,sin \, \theta = 4 \times \frac{3}{5} = \frac{12}{5}$