# Geometry Problem 1520: Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge. Difficulty Level: High School.

In a rectangle ABCD, E is an exterior point such that AC and DE measure
24 units each, and angles CAD and CDE are congruent. Calculate BE. See
the figure or diagram below.

## Definitions and Suggestions

Theorem |
Description |

Rectangle |
In a rectangle, opposite sides are congruent and parallel.
The diagonals of a rectangle are congruent.
The diagonals of a rectangle bisect each other. |

Congruent Angles |
Congruent angles are angles that have the same measure. |

45-45-90 Triangle |
A 45-45-90 triangle is a right triangle with two legs that are
congruent and a hypotenuse that is √2 times the length of a leg. |

###
Thematic Poem:

Journey of Geometry: Discovering Distances in a Rectangle with an Exterior Point

Discovering distances in a rectangle so fair,

With an exterior
point beyond compare,

Geometry challenges waiting to be found,

A
journey of discovery, unbound.

Congruent segments beckon with delight,

Angles matching in a
perfect sight,

BD and DE measure 24 each,

A puzzle to solve,
within our reach.

CAD and CDE congruent and true,

A fascinating problem for me and
you,

Together we will find the length of BE,

A journey of
learning, for us to see.

So let us embark on this geometry quest,

A challenge so great, we
won't rest,

Discovering distances, angles, and more,

In a
rectangle, with an exterior point to explore.