Three Dimensional Geometry Question 37
Question: If two spheres of radii $ r_1 $ and $ r_2 $ cut orthogonally, then the radius of the common circle is
Options:
A) $ r_1r_2 $
B) $ \sqrt{(r_1^{2}+r_2^{2}}) $
C) $ r_1r_2\sqrt{(r_1^{2}+r_2^{2})} $
D) $ \frac{r_1r_2}{\sqrt{(r_1^{2}+r_2^{2})}} $
Show Answer
Answer:
Correct Answer: D
Solution:
In $ \Delta OPC $ , $ \cos \theta =\frac{r}{r_1} $ In $ \Delta O’PC $ , $ \sin \theta =\frac{r}{r_2} $ As, $ {{\cos }^{2}}\theta +{{\sin }^{2}}\theta =1 $ \ $ {{( \frac{r}{r_1} )}^{2}}+{{( \frac{r}{r_2} )}^{2}}=1 $ Þ $ r=\frac{r_1r_2}{\sqrt{r_1^{2}+r_2^{2}}} $ .
BETA
