WOLFRAM|DEMONSTRATIONS PROJECT

Fagnano's Problem

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show altitudes
R
0.59
S
0.5
T
0.4
DE
≈
9.39
EF
≈
5.63
DF
≈
7.66
RS
≈
8.05
ST
≈
7.42
RT
≈
8.61
perimeter(DEF)
≈
22.68
perimeter(RST)
≈
24.08
Let ABC be an acute triangle. Let D, E, and F be the points where the altitudes from A, B, and C intersect the sides of the triangle. Then DEF is the inscribed triangle of smallest perimeter.