MathDB
isosceles triangle construction given 2 incircles

Source: 2019 XXII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p9

May 4, 2021
constructionisoscelesinradiusgeometryUkrainian TYM

Problem Statement

On the base BCBC of the isosceles triangle ABCABC chose a point DD and in each of the triangles ABDABD and ACDACD inscribe a circle. Then everything was wiped, leaving only two circles. It is known from which side of their line of centers the apex AA is located . Use a compass and ruler to restore the triangle ABCABC , if we know that : a) ADAD is angle bisector, b) ADAD is median.