Question

Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is

• A. \(\sqrt{2}\)
• B. \(\frac{\pi}{3}\)
• C. \(\frac{1}{\sqrt{2}}\)
• D. 1

Answer 1

The Correct Option is D

From the figure

SO=4-r.
Applying the Pythagorean theorem to triangle POS, we obtain:
\((4+r)^2=4^2+(4−r)^2\)
\(⇒(4+r)^2−(4−r)^2=16\)
\(⇒4×4×r=16\)
\(⇒r=1\)