WOLFRAM|DEMONSTRATIONS PROJECT

The Sum of the Distances from the Orthocenter to the Vertices

HA

≈

5.16

HB

≈

2.13

HC

≈

4.64

R

≈

4.04

r

≈

1.92

HA

+

HB

+

HC

≈

11.93

2

(

R

+

r

)

≈

11.93

The intersection of the altitudes of a triangle is called the orthocenter.

Let H be the orthocenter of the triangle ABC, and let

R

and

r

be its circumradius and inradius. When H lies inside ABC, HA + HB + HC = 2 (

R

+

r

).