Geometry Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square - A High School Challenge

Consider a square ABCD with center O. Suppose an exterior triangle AEB is constructed such that angle AEB measures 90 degrees and angle ABE measures 53 degrees. The line EO is extended to intersect side CD at a point F. Find the measure of angle OFC.

Geometry Problem 1533: Uncover the relationship between angles in an exterior triangle and intersecting lines of a square

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Thematic Poem:
Geometric Beauty: Discovering Cyclic Quadrilaterals and Angles in a Square

In a geometry problem, one may find,
A square with angles all aligned,
But a triangle on the outside,
Will make your geometric heart glide.

For angles of the triangle,
Will reveal what you need to see,
When lines intersect with such grace,
You'll see a cyclic quadrilateral take place.

The center of the square is where it's at,
It's where you'll find lines that match,
When extended beyond their length,
You'll find new angles with great strength.

So uncover the relationship true,
Between angles and lines that ensue,
For a geometric problem so fine,
Is where your love for math will shine.

If you're interested in finding more poems with a focus on geometry, you may enjoy this collection: More geometry thematic poems.

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