MathDB

Triangle altitudes

Source: 2002 China Second Round Olympiad

August 30, 2014

geometrycircumcircletrigonometry

Problem Statement

In

\triangle ABC

,

\angle A = 60

,

AB>AC

, point

O

is the circumcenter and

H

is the intersection point of two altitudes

BE

and

CF

. Points

M

and

N

are on the line segments

BH

and

HF

respectively, and satisfy

BM=CN

. Determine the value of

\frac{MH+NH}{OH}

.

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