Radius and Construction of a Mixtilinear Circle
What is this about?
A Mathematical Droodle
r = rAcos2(α/2),
where α = ∠BAC, r is the radius of the incircle of ΔABC and rA is the radius of the mixtilinear incircle inscribed into angle BAC.
The construction is this: first draw a perpendicular to the bisector of ∠BAC through the incenter I. This line will meet the sides AB and AC in points D and E. Second, draw a perpendicular to AB at D and a perpendicular to AC at E. These these two lines will meet again on the bisector of ∠BAC in the center of the mixtilinear incircle touching AB and AC.
An explanation for the construction can be found on a separate page.
- P. Yiu, Mixtilinear Circles, Am Math Monthly, v. 106, n. 10 (Dec., 1999), 952-955
- P. Yiu, Notes on Euclidean Geometry, 1998, pp. 56-57