Article 6RGBY Relating six properties of a triangle in one equation

Relating six properties of a triangle in one equation

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John
from John D. Cook on (#6RGBY)

in_out_triangle.png

Let a, b, and c be the sides of a triangle.

Let p be perimeter of the triangle.

Let r be the radius of the largest circle that can be inscribed in the triangle, and let R be the radius of the circle through the vertices of the triangle.

Then all six numbers can be related in one equation:

2prR = abc.

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