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1. A triangle with sides 13 cm, 14 cm and 15 cm is inscribed in a circle. The radius of the circle is :

A. 2 cm

B. 3 cm

C. 4 cm

D. 8.125 cm

Solution:

\begin{aligned} s = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21 \\ ∴ △ = \sqrt{21 \times 8 \times 7 \times 6} \\ = \sqrt{s (s - a) (s - b) (s - c)} \\ = (2 \times 2 \times 3 \times 7) \\ = 84 c m^{2} \end{aligned}

Radius of circle :

\begin{aligned} = (\frac{13 \times 14 \times 15}{4 \times 84}) c m^{2} \\ = (\frac{65}{8}) c m \\ = 8.125 c m \end{aligned}

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