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9
SMT 2010 Geometry #9
SMT 2010 Geometry #9
Source:
February 11, 2012
geometry
circumcircle
incenter
trigonometry
algebra
system of equations
Problem Statement
For an acute triangle
A
B
C
ABC
A
BC
and a point
X
X
X
satisfying
∠
A
B
X
+
∠
A
C
X
=
∠
C
B
X
+
∠
B
C
X
\angle{ABX}+\angle{ACX}=\angle{CBX}+\angle{BCX}
∠
A
BX
+
∠
A
CX
=
∠
CBX
+
∠
BCX
.Fi nd the minimum length of
A
X
AX
A
X
if
A
B
=
13
AB=13
A
B
=
13
,
B
C
=
14
BC=14
BC
=
14
, and
C
A
=
15
CA=15
C
A
=
15
.
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