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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
4 years 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.

Yong See Foo - 4 years ago

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