MathDB
2024 COMC C3

Source:

November 4, 2024
Comc

Problem Statement

Let ABCABC be a triangle for which the tangent from AA to the circumcircle intersects line BCBC at DD, and let OO be the circumcenter. Construct the line ll that passes through AA and is perpendicular to ODOD. ll intersects ODOD at EE and BCBC at FF. Let the circle passing through ADOADO intersect BCBC again at HH. It is given that AD=AO=1AD=AO=1.
a) Find OEOE b) Suppose for this part only that FH=112FH=\frac{1}{\sqrt{12}}: determine the area of triangle OEFOEF. c) Suppose for this part only that BC=3BC=\sqrt3: determine the area of triangle OEFOEF. d) Suppose that BB lies on the angle bisector of DEFDEF. Find the area of the triangle OEFOEF.
Back to ProblemsView on AoPS