MathDB

MOP [Points on the sides of the orthic triangle]

Source: also: Singapore TST (which year?)

October 8, 2003

trigonometrygeometryangle bisectorgeometry solved

Problem Statement

Let

A_{1}

B_{1}

C_{1}

be the feet of the altitudes of an acute-angled triangle

ABC

issuing from the vertices

A

B

C

, respectively. Let

K

and

M

be points on the segments

A_{1}C_{1}

and

B_{1}C_{1}

, respectively, such that

\measuredangle KAM = \measuredangle A_{1}AC

. Prove that the line

AK

is the angle bisector of the angle

C_{1}KM