# Radius and Construction of a Mixtilinear Circle What is this about? A Mathematical Droodle

Explanation The applet illustrates a simple construction of a mixtilinear circle based on a formula

(1)

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. ### References

1. P. Yiu, Mixtilinear Circles, Am Math Monthly, v. 106, n. 10 (Dec., 1999), 952-955
2. P. Yiu, Notes on Euclidean Geometry, 1998, pp. 56-57 ### Mixtilinear Incircles

• Mixtilinear Circles and Concurrence
• Sangakus with a Mixtilinear Circle
• Sangaku with Three Mixtilinear Circles
• Construction and Properties of Mixtilinear Incircles
• Construction and Properties of Mixtilinear Incircles 2
• Conic in Mixtilinear Incircles
• A Sangaku: Two Unrelated Circles
• 