question_answer

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) \[\sqrt{12}\]

Correct Answer: B

Solution :

[b] For the orthogonal section \[{{C}_{1}}P\] and \[{{C}_{2}}P\] are pendicular where \[{{C}_{1}}\]and \[{{C}_{2}}\] are centers 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 \[OP={{C}_{1}}P\sin \theta =4\times \frac{3}{5}=\frac{12}{5}\]