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)

For the orthogonal section $C_{1}P$ and $C_{2}P$ are pendicular where $C_1$ and $C_2$ are centres of sphere of radii $4$ and $3$ respectively
Now $C_{1}P=4$ and $C_{2}P=3$, so $tan\theta =\frac{3}{4}$
$\therefore$ Radius of circle of intersection
$OP=C_{1}Psin\theta =4\times \frac{3}{5}=\frac{12}{5}$