Steiner's Theorem

Given: any triangle ABC

Circumradius: R

Inradius: r

Exradius: ra, rb, rc

To prove:

ra+ rb+ rc - r = 4R

Proof:

1. MH + HN = 2R

    H midpoint KG

    H midpoint LQ

2. MH = 1/2(ra+ rb)

3. HN = 1/2(rc - r)