MathDB
Colinear Points

Source: 2016 Korea Winter Camp 2nd Test #2

January 25, 2016
geometry

Problem Statement

Let there be an acute triangle ABCABC, such that ∠ABC<∠ACB\angle ABC < \angle ACB. Let the perpendicular from AA to BCBC hit the circumcircle of ABCABC at DD, and let MM be the midpoint of ADAD. The tangent to the circumcircle of ABCABC at AA hits the perpendicular bisector of ADAD at EE, and the circumcircle of MDEMDE hits the circumcircle of ABCABC at FF. Let GG be the foot of the perpendicular from AA to BDBD, and NN be the midpoint of AGAG. Prove that B,N,FB, N, F are collinear.
Back to ProblemsView on AoPS