Home Geometry Problems All Problems 331-340 Circle Inscribed in a Square View or post a solution 
Problem 331. Discovering the Relationship between Distances from a Point on the Inscribed Circle to Tangency Point and Vertices in a Square.
Level: High School, College, SAT Prep.

The figure shows a square ABCD with P on the inscribed circle O. If E, F, G, and H are the tangency points, prove that Problem 331 conclusion to prove.

Square, inscribed circle

Thematic Poem: Unraveling the Mystery: The Relationship Between Points on an Inscribed Circle and Tangency Points in a Square

Amidst the squares and angles of our minds,
Lies a mystery waiting to be found,
A hidden path that none yet unwinds,
A puzzle yet to be unbound.

Discovering the relationship between,
Distances of a point on circle's arc,
To tangency points and vertices seen,
A revelation, a brand-new spark.

The inscribed circle, a central guide,
With its point in question, a starting place,
We take a journey with eyes open wide,
And unravel a puzzle with skill and grace.

With each step forward, we find a clue,
And piece by piece, the picture emerges clear,
A new perspective that once was askew,
Now seen with clarity, without a single tear.

The distance to vertices, the tangency points,
All speak to us in silent code,
A language that our heart anoints,
As we walk the path, on this quest we strode.

The thrill of discovery, a journey worthwhile,
A quest that feeds the mind and soul,
The beauty of numbers, an endless pile,
As we uncover mysteries, a story untold.

In this journey, we find a new friend,
A geometry that speaks to us in rhyme,
A love for numbers, that never ends,
And a journey that transcends time.


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