Conic Construction of a Triangle from the Feet of Its Angle Bisectors
نویسندگان
چکیده
We study an extension of the problem of construction of a triangle from the feet of its internal angle bisectors. Given a triangle ABC, we give a conic construction of points P which are the incenter or excenters of their own anticevian triangles with respect to ABC. If the given triangle contains a right angle, a very simple ruler-and-compass construction is possible. We also examine the case when the feet of the three external angle bisectors are three given points on a line. 1. The angle bisectors problem In this note we address the problem of construction of a triangle from the endpoints of its angle bisectors. This is Problem 138 in Wernick’s list [2]. The corresponding problem of determining a triangle from the lengths of its angle bisectors have been settled by Mironescu and Panaitopol [1]. A
منابع مشابه
Some Geometric Inequalities Involving Angle Bisectors and Medians of a Triangle
In the present paper some geometric inequalities concerning the angle bisectors and the medians of a triangle are established. Mathematics subject classification (2010): Primary 26D15.
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