No! That's cheating

Geometry Level 3

Two circles with radii a a and b b touch each other externally.Let c c be the radius of a circle which touches these two circles as well as the common tangent to the two circles.Then,

1 c = 1 a + 1 b \dfrac{1}{\sqrt{c}}=\dfrac{1}{\sqrt{a}}+\dfrac{1}{\sqrt{b}} c = a + b \sqrt{c}=\sqrt{a}+\sqrt{b} 1 c = a b \dfrac{1}{\sqrt{c}}=\sqrt{ab} c = a b c=\sqrt{ab}

A Former Brilliant Member by A Former Brilliant Member

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