## Assignement 6:

# Connecting Two Classes with One
Problem

#### By

### Jen Curro

The problem I chose to do for this write-up
is both a choice for Assignment 6 and a problem to be solved in
the EMAT 6600 Problem Solving Class. The problem is also found
in *Mathematical Discovery *by George Polya.

Given three points A, B, and C. Draw a
line intersecting segment AC and BC where X is a point on AC and
Y is a point on BC where AX=XY=YB

This picture will look something like
this in the end:

The first step is to pick some point D
on segment BC. This point is a random point on BC but should not
be too far from C.

Next draw a line, DE parallel to segment
AB, that is the same length as DC.

Next construct point F on the segment
AC so that CD=DE=EF

Next, connect segment CE and extend CE
down to a point G on segment AB.

Now draw a line parallel to EF through
A.

The intersection of this line and segment
DE is H

Now when D is moved along the BC segment,
the position of both H and F move accordingly. Therefore when
D is at a spot on BC, such that F and A are the same point and
H and E are the same point this spot for D will be called X.

At this point the circle drawn from the
center point X and intersects segment AB is the other point Y
that is needed.

To play more with the illustration, click here. (Must have GSP)

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