The Triangles Cut Off by the Sides of the Orthic Triangle

​
∠BAC
≈
50.30°
∠ABC
≈
74.72°
∠ACB
≈
54.97°
∠C'AB'
≈
50.30°
∠AB'C'
≈
74.72°
∠AC'B'
≈
54.97°
∠BA'C'
≈
50.30°
∠A'BC'
≈
74.72°
∠BC'A'
≈
54.97°
∠CA'B'
≈
50.30°
∠CB'A'
≈
74.72°
∠A'CB'
≈
54.97°
Let ABC be a triangle. The triangle formed by the endpoints of the altitudes is called the orthic triangle of ABC.
The triangles cut off by the sides of the orthic triangle are similar to the original triangle.

Details

See theorem 184 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 97.

External Links

Orthic Triangle (Wolfram MathWorld)
Similar Triangles (Wolfram MathWorld)

Permanent Citation

Jay Warendorff
​
​"The Triangles Cut Off by the Sides of the Orthic Triangle"​
​http://demonstrations.wolfram.com/TheTrianglesCutOffByTheSidesOfTheOrthicTriangle/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011