Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.2 Junior Find the answer

A triangle is circumscribed about a circle of radius $r$ inches. If the perimeter of the triangle is $P$ inches and the area is $K$ square inches, then $\frac{P}{K}$ is:

Pick one

Solution

The area $K$ of the triangle can be expressed in terms of its inradius $r$ and its semiperimeter $s$ as:
$K = r \times s = r \times \frac{P}{2}$
So, $\frac{P}{K} = \boxed{\textbf{(C) } \frac{2}{r}}$ .
~ proloto

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