Question:

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

Updated On: Jul 7, 2022
  • $12$
  • $ \frac{12}{5}$
  • $ \frac{\sqrt{12}}{5}$
  • $ \sqrt{12}$
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The Correct Option is B

Solution and Explanation

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 $OP = C_{1}P \,sin \, \theta = 4 \times \frac{3}{5} = \frac{12}{5}$
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