MathDB
Turkey Junior Olympiad 2005, Part II - P1

Source:

January 20, 2013
geometrycircumcircleratio

Problem Statement

Let ABCABC be an acute triangle. LetHH and DD be points on [AC][AC] and [BC][BC], respectively, such that BH⊥ACBH \perp AC and HD⊥BCHD \perp BC. Let O1O_1 be the circumcenter of △ABH\triangle ABH, and O2O_2 be the circumcenter of △BHD\triangle BHD, and O3O_3 be the circumcenter of △HDC\triangle HDC. Find the ratio of area of △O1O2O3\triangle O_1O_2O_3 and △ABH\triangle ABH.
Back to ProblemsView on AoPS