MathDB

Angle chasing in triangle

Source: Canada 1998

March 4, 2006

trigonometrygeometrycircumcircletrig identitiesLaw of Sinesgeometry unsolved

Problem Statement

Let

ABC

be a triangle with

\angle{BAC} = 40^{\circ}

and

\angle{ABC}=60^{\circ}

. Let

D

and

E

be the points lying on the sides

AC

and

AB

, respectively, such that

\angle{CBD} = 40^{\circ}

and

\angle{BCE} = 70^{\circ}

. Let

F

be the point of intersection of the lines

BD

and

CE

. Show that the line

AF

is perpendicular to the line

BC

.

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