3 Cheers for Geometry !!

Geometry Level 5

The sides a,b,c of a Δ \Delta ABC are in Geometric Progression whose common ratio is 23 \frac{2}{3} and the circumradius of the triangle is 6×7209 6 \times \sqrt{ \frac{7}{209}} .

Find the longest side of the triangle .

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

Find mn m^{n} .

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