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Geometry Level 3

A circle of radius 4 cm is circumscribed by a triangle of perimeter 26 cm. Find the area of the triangle.(in cm)

If finding the area is not possible type − 1 -1 as your answer.


The answer is 52.

Manan Maheshwari by Manan Maheshwari , 20, India

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1 solution

Area of triangle = semiperimeter of triangle x inradius =13 x 4 = 52 (In this case, the triangle is circumscribed to the circle), but does there really exists this triangle? I don't think so

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Can you prove that area of triangle is semiperimeter * inradius?

Manan Maheshwari - 5 years, 4 months ago

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I can give you one directriz, divide the triangle at three smaller triangles from the incentre to the vertices of the original triangle. In each one of these smaller triangles we can take the base to be one side of the original triangle , then the height of these 3 triangles is the inradius... One question is, does there really exits this triangle? I don't think so

Guillermo Templado - 5 years, 4 months ago

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Yeah such a triangle will exist but the sides will be irrational

Manan Maheshwari - 5 years, 4 months ago

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