MathDB

3

Part of 2010 Regional Competition For Advanced Students

Problems(1)

∆ABC and ∆AUV are similar

Source:

4/26/2010
Let △ABC\triangle ABC be a triangle and let DD be a point on side BC‾\overline{BC}. Let UU and VV be the circumcenters of triangles △ABD\triangle ABD and △ADC\triangle ADC, respectively. Show, that △ABC\triangle ABC and △AUV\triangle AUV are similar.
(41th Austrian Mathematical Olympiad, regional competition, problem 3)
geometrycircumcirclegeometry proposed