Mental Ability Olympiad Question on circles X grade

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
5 years, 10 months ago

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Hint: Pythagorean's formula. Let the points of contact between the circle and the common tangent be TA,TB,TCT_A, T_B, T_C. Find TATB,TATC,TCTBT_AT_B, T_AT_C, T_CT_B in terms of a,b,ca,b,c. Anyway draw a figure yourself.

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