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

Explanation

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Copyright © 1996-2018 Alexander Bogomolny

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.

illustration of the construction of mixtilinear circle

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
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|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny
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