# Radius and Construction of a Mixtilinear Circle

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A Mathematical Droodle

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Copyright © 1996-2018 Alexander BogomolnyThe applet illustrates a simple construction of a mixtilinear circle based on a formula

(1)

r = r_{A}cos^{2}(α/2),

where α = ∠BAC, r is the radius of the incircle of ΔABC and r_{A} 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

- 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

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