MathDB

ABC is an Acute Triangle

Source: CentroAmerican 2013 Problem 5

August 24, 2013

trigonometrygeometryangle bisectortrig identitiesLaw of Sinesgeometry unsolved

Problem Statement

Let

ABC

be an acute triangle and let

\Gamma

be its circumcircle. The bisector of

\angle{A}

intersects

BC

D

\Gamma

K

(different from

A

), and the line through

B

tangent to

\Gamma

X

. Show that

K

is the midpoint of

AX

if and only if

\frac{AD}{DC}=\sqrt{2}