MathDB

2

Part of 1997 Irish Math Olympiad

Problems(2)

locus

Source: Ireland 1997

7/3/2009
For a point M M inside an equilateral triangle ABC ABC, let D,E,F D,E,F be the feet of the perpendiculars from M M onto BC,CA,AB BC,CA,AB, respectively. Find the locus of all such points M M for which ∠FDE \angle FDE is a right angle.
geometry proposedgeometry
find the length

Source: Ireland 1997

7/3/2009
A circle Γ \Gamma is inscribed in a quadrilateral ABCD ABCD. If \angle A\equal{}\angle B\equal{}120^{\circ}, \angle D\equal{}90^{\circ} and BC\equal{}1, find, with proof, the length of AD AD.
trigonometrygeometry proposedgeometry