Three Dimensional Geometry Question 146
Question: Two spheres of radii 3 and 4 cut orthogonally The radius of common circle is
Options:
A) 12
B) $ \frac{12}{5} $
C) $ \frac{\sqrt{12}}{5} $
D) $ \sqrt{12} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] For the orthogonal section $ C_1P $ and $ C_2P $ are pendicular where $ C_1 $ and $ C_2 $ are centers 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_1P\sin \theta =4\times \frac{3}{5}=\frac{12}{5} $
BETA
