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  4. In a triangle ABC the lengths of AB , BC and CA are 13,14 and 15 units respectively. The altitudes of the triangle ABC are concurrent at the point H and AD is the altitude on BC. The circum radius of the triangle ABC is

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Q. In a triangle $ABC$ the lengths of $AB , BC$ and $CA$ are 13,14 and 15 units respectively. The altitudes of the triangle $ABC$ are concurrent at the point $H$ and $AD$ is the altitude on $BC$.
The circum radius of the triangle $ABC$ is

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Solution:

Area of triangle $ABC =\frac{5 \cdot 12+12 \cdot 9}{2}=30+54=84$
$\therefore R =\frac{ abc }{4 \Delta}=\frac{13 \cdot 14 \cdot 15}{4 \cdot 84} $
$R =\frac{13 \cdot 15}{4 \cdot 6}=\frac{65}{8} \Rightarrow (B)$

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