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1
HMMT Team 2019/1: Affine geometry
HMMT Team 2019/1: Affine geometry
Source:
February 17, 2019
HMMT
geometry
analytic geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram. Points
X
X
X
and
Y
Y
Y
lie on segments
A
B
AB
A
B
and
A
D
AD
A
D
respectively, and
A
C
AC
A
C
intersects
X
Y
XY
X
Y
at point
Z
Z
Z
. Prove that
A
B
A
X
+
A
D
A
Y
=
A
C
A
Z
.
\frac{AB}{AX} + \frac{AD}{AY} = \frac{AC}{AZ}.
A
X
A
B
+
A
Y
A
D
=
A
Z
A
C
.
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