WOLFRAM|DEMONSTRATIONS PROJECT

Products of Segments of Altitudes

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AH
≈
0.90
HA'
≈
0.69
BH
≈
1.33
HB'
≈
0.47
CH
≈
1.18
HC'
≈
0.52
AH
×
HA'
≈
0.62
BH
×
HB'
≈
0.62
CH
×
HC'
≈
0.62
Let ABC be a triangle, let AA', BB', and CC' be the altitudes, and let H be the orthocenter, the intersection of the altitudes. Then AH×HA' = BH×HB' = CH×HC'.