Two circles with radii a and b respectively touch each other externally. Let c be the radius of a circle that touches these two circles as well as a common tangent to these two circles . Then _. (No figure given)

(A) 1 upon root a - 1 upon root b = 1 upon root c (B) 1 upon root a + 1 upon root b + 1 upon root c = 0 (C) 1 upon root a + 1 upon root b = 1 upon root c (D) none of these

The answer is C but how?

Note by Pranjal Kulkarni
4 years, 9 months ago

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Hint: Pythagorean's formula. Let the points of contact between the circle and the common tangent be $$T_A, T_B, T_C$$. Find $$T_AT_B, T_AT_C, T_CT_B$$ in terms of $$a,b,c$$. Anyway draw a figure yourself.

- 4 years, 9 months ago