Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.3 Junior Find the answer

In a triangle, the area is numerically equal to the perimeter. What is the radius of the inscribed circle?

Pick one

Solution

One of the most common formulas involving the inradius of a triangle is $A = rs$ , where $A$ is the area of the triangle, $r$ is the inradius, and $s$ is the semiperimeter.
The problem states that $A = p = 2s$ . This means $2s = rs$ , or $r = 2$ , which is option $\fbox{A}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.