Radical center

pestich · Poincare Conjecture Offline Joined: 03 Mar 2004 Posts: 181

Identify triangle center where the radical lines of three mixtilinear circles (tangent to 2 sides of triangle ABC
and internally to it's circumcircle) concur.

Maj. Pestich

**Posted:** Fri Jan 28, 2005 12:34 pm

darij grinberg

Paul Yiu, Mixtilinear Incircles, II, paragraph 1, Theorem 1:

The radical center of the three mixtilinear incircles of a triangle is the point P dividing the segment OI externally in the ratio $OP:PI=R:\left(-\frac{r}{2}\right)$ .

Hereby, of course, O is the circumcenter, I is the incenter, R is the circumradius and r is the inradius of triangle ABC.

See also Paul Yiu, Mixtilinear Incircles, III.

Darij

**Posted:** Fri Jan 28, 2005 12:45 pm

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