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Question

Quantitative Aptitude Question on Triangles, Circles & Quadrilaterals

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

2\sqrt{2}

B

π3\frac{\pi}{3}

C

12\frac{1}{\sqrt{2}}

D

1

Answer

1

Explanation

Solution

From the figure
Pythagoras theorem in triangle POS
SO=4-r.
Applying the Pythagorean theorem to triangle POS, we obtain:
(4+r)2=42+(4−r)2(4+r)^2=4^2+(4−r)^2
⇒(4+r)2−(4−r)2=16⇒(4+r)^2−(4−r)^2=16
⇒4×4×r=16⇒4×4×r=16
⇒r=1⇒r=1