WOLFRAM|DEMONSTRATIONS PROJECT

The Area of a Triangle, its Circumradius, and the Perimeter of its Orthic Triangle

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A'B'
≈
3.80
B'C'
≈
3.97
A'C'
≈
2.05
p
≈
9.82
α
≈
19.85
R
≈
4.04
p
×
R
≈
39.69
2
α
≈
39.69
Let ABC be an acute triangle and A'B'C' be its orthic triangle (the triangle formed by the endpoints of the altitudes of ABC). Let
p
be the perimeter of A'B'C',
R
be the circumradius of ABC, and
α
be the area of ABC. Then
p×R=2α
.