Relating six properties of a triangle in one equation

Triangle with inscribed and circumscribed circles

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.

 

2 thoughts on “Relating six properties of a triangle in one equation

  1. Dr Cook,
    Thanks love the way we can use there together. But, am I missing something? The equation appears to be off by a factor of 2.
    Should be 4prR = abc

  2. Perhaps you’re thinking of the equation in the form 4srR = abc where s is the semiperimeter, s = p/2.

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