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Largest circle in a triangle

MediumBrainteasers~5m

What is the area of the largest circle that fits inside a triangle with side lengths 1616, 1616, and 2424? The area can be written as pπq\dfrac{p\pi}{q} with pq\dfrac{p}{q} in lowest terms. What is p+qp + q?

Show hints (2)+
  1. The largest circle inside a triangle is its incircle, with radius r=(area)/(semiperimeter)r = (\text{area})/(\text{semiperimeter}).
  2. Get the area from Heron's formula (or the isosceles height), then compute πr2\pi r^2.

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