MathDB

6

Part of 2021 Oral Moscow Geometry Olympiad

Problems(2)

MH intersects the angle bisector

Source: 2021 Oral Moscow Geometry Olympiad grades 8-9 p6

5/17/2021
Point MM is a midpoint of side BCBC of a triangle ABCABC and HH is the orthocenter of ABCABC. MHMH intersects the AA-angle bisector at QQ. Points XX and YY are the projections of QQ on sides ABAB and ACAC. Prove that XYXY passes through HH.
geometryangle bisectororthocenter
An equilateral triangle inscribed in a square

Source: 2021 Oral Moscow Geometry Olympiad grades 10-11 p6

5/17/2021
ABCDABCD is a square and XYZXYZ is an equilateral triangle such that XX lies on ABAB, YY lies on BCBC and ZZ lies on DADA. Line through the centers of ABCDABCD and XYZXYZ intersects CDCD at TT. Find angle CTYCTY
geometrysquareEquilateral Trianglehard