Geometry Problem 1495: Unlocking the Mysteries of Circles: Proving the Relationship Between Parallel Chords, 30 degrees and Radius

A circle with radius r has chords AB, CD, and EF parallel to each other, as well as chords AD and CF parallel to each other. See figure for visualization. You are required to prove that \({AB^2+CD^2+EF^2} = {6\cdot r^2}\).

Geometry Problem 1495: Circle, Parallel Chords, 30 Degree Angle, Square

View solution

Typography and Sketch: Exploring Problem 1495 with Machu Picchu in the Background

Geometry Problem 1495: Circle, Parallel Chords, 30 Degree Angle, Square, Machu Picchu in the background

Geometric Art using Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.

Thematic Poem:
Geometry Problem 1495: Tips and Strategies for Successful Problem Solving

Within a circle, chords do lie,
Parallel to each other they lie.
AB, CD, and EF, they go,
AD and CF, they also show.

Radius r is what we know,
But the rest is yet to show.
To prove a relationship true,
A challenge lies in front of you.

With angles 30 degrees and more,
And a sum of squares to explore,
The puzzle seems complex and deep,
But in geometry, secrets we shall reap.

Look to the figure, visualize,
And let your reasoning arise.
For in the end, with diligence and care,
The solution to the mystery will be there.

Unlock the secrets of the circle's lore,
Prove the relationship once and for all.
With math and wit, we shall prevail,
And in geometry, our knowledge shall prevail.

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

Recent Additions

Geometry Problems
Open Problems
Visual Index
Ten problems: 1411-1420
All Problems
Angle: 30 degrees
Parallel lines
View or Post a solution

Search our site with Google:

Geometry Problem 1495 Solution(s)