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Part of 2005 Turkey Junior National Olympiad

Problems(1)

Turkey Junior Olympiad 2005, Part II - P1

Source:

1/20/2013
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.
geometrycircumcircleratio