WOLFRAM|DEMONSTRATIONS PROJECT

The Distance to the Orthocenter from a Vertex

​
AH
≈
4.19
BC
≈
13.32
OA
≈
6.98
2
AH
+
2
BC
≈
194.93
4
×
2
OA
≈
194.93
Let ABC be a triangle and H its orthocenter. Let O and
R
be the circumcenter and circumradius of ABC. Then
2
AH
+
2
BC
=4
2
R
.