Intersection of an Altitude and a Line through the Incenter

AE

≈

4.90

r

≈

4.90

Let ABC be a triangle with incenter I and inradius

r

. Let M be the midpoint of BC, H the foot of the altitude drawn from A, and E the intersection of MI with AH. Then

AE=r

.

Details

See problem 5.7 in V. Prasolov, Problems in Plane and Solid Geometry , Vol. 1, Plane Geometry[PDF], (D. Leites, ed. and trans.).

External Links

Incenter (Wolfram MathWorld)

Inradius (Wolfram MathWorld)

Midpoint (Wolfram MathWorld)

Permanent Citation

Jay Warendorff

"Intersection of an Altitude and a Line through the Incenter"
http://demonstrations.wolfram.com/IntersectionOfAnAltitudeAndALineThroughTheIncenter/
Wolfram Demonstrations Project
Published: March 7, 2011