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.
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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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