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The harmonic mean of the three ex - radii (in ems) of a triangle with inradius $1 c m$ and circumradius $3 c m$ . is

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$\frac{1}{3}$

$\frac{2}{3}$

answer is B.

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Detailed Solution

$r = \frac{Δ}{s}, r_{1} = \frac{Δ}{s - a}, \dots \dots$

$\begin{array}{l} ∴ H.M of ex - radii = \frac{3}{\sum \frac{1}{r}} = \frac{3}{\sum (s - a)} \\ = \frac{3 Δ}{s} = 3 r = 3 \end{array}$

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