WOLFRAM|DEMONSTRATIONS PROJECT

Triangle Altitudes and Circumradius

​
AA'×BB'×CC'
≈
122.
2
(BC×AC×AB)
8
3
circumradius
≈
122.
If ABC is a triangle with side lengths
a
,
b
, and
c
, altitudes
α
,
β
, and
γ
, and circumradius
R
, then
αβγ=
2
(abc)
8
3
R
.