# 3 Cheers for Geometry !!

Geometry Level 5

The sides a,b,c of a $\Delta$ABC are in Geometric Progression whose common ratio is $\frac{2}{3}$ and the circumradius of the triangle is $6 \times \sqrt{ \frac{7}{209}}$ .

Find the longest side of the triangle .

The answer is of the form $\frac{m}{n}$ where m and n are co-prime numbers ;

Find $m^{n}$ .

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