MathDB

3

Part of 2010 Moldova Team Selection Test

Problems(2)

Find angle

Source: Moldova TST 2010, day 1, problem 3

3/3/2010
Let ABCD ABCD be a convex quadrilateral. We have that \angle BAC\equal{}3\angle CAD, AB\equal{}CD, \angle ACD\equal{}\angle CBD. Find angle ∠ACD \angle ACD
trigonometrygeometry proposedgeometry
Isosceles triangle with height $HM$

Source: Moldova TST 2010, day 2, problem 3

3/4/2010
Let ABC ABC be an acute triangle. H H is the orthocenter and M M is the middle of the side BC BC. A line passing through H H and perpendicular to HM HM intersect the segment AB AB and AC AC in P P and Q Q. Prove that MP \equal{} MQ
geometryratioparallelogramperpendicular bisectorgeometry proposed