Euler Triangle Formula/Corollary

Theorem

Let $\rho$ be the inradius of a triangle.

Then:

$\dfrac 1 \rho = \dfrac 1 {R - d} + \dfrac 1 {R + d}$

where:

$R$ is the circumradius

$d$ is the distance between the incenter and the circumcenter.

Proof

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Source of Name

This entry was named for Leonhard Paul Euler.