MathDB

2

Part of 2013 Oral Moscow Geometry Olympiad

Problems(2)

triangle split into 2 triangles with same sum of squares of sides

Source: 2013 Oral Moscow Geometry Olympiad grades 8-9 p2

8/14/2019
With a compass and a ruler, split a triangle into two smaller triangles with the same sum of squares of sides.
constructiongeometrycompassRuler
intersection point of internal common tangent lies on angle bisector

Source: 2013 Oral Moscow Geometry Olympiad grades 10-11 p2

8/16/2019
Inside the angle AODAOD, the rays OBOB and OCOC are drawn such that ∠AOB=∠COD.\angle AOB = \angle COD. Two circles are inscribed inside the angles ∠AOB\angle AOB and ∠COD\angle COD . Prove that the intersection point of the common internal tangents of these circles lies on the bisector of the angle AODAOD.
common tangentsinscribed circlesangle bisectorequal anglesgeometry