Geometry Problem 1535: Crack the Code: Inscribed Circle in Square - Angle Challenge! Solve the Mystery

In a square ABCD, a circle with center O is inscribed, such that it touches sides AB, BC, CD, and AD at points E, F, G, and H, respectively. The line BD intersects the arc EF at point K. The lines AF and HK intersect at point M. Calculate the measure of angle AMK.

Geometry Problem 1535: Crack the Code: Inscribed Circle in Square - Angle Challenge! Solve the Mystery

View or post a solution

Recent Additions

Geometry Problems
Open Problems
Visual Index
All Problems
Circle Tangent Line
Perpendicular lines
Special Right Triangle
Thematic Poems
View or Post a solution 

Illustrating Problem 1535: A Creative Poster Using iPad Apps

Geometry Problem 1535: Crack the Code: Inscribed Circle in Square - Angle Challenge! Solve the Mystery, iPad app!


Discover Even More: See Also...

Problem 1536

Geometry Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals

Problem 1534

Geometry Problem 1534: High School Brainteaser: Tangent Circles, Common External Tangent, and Angle Conundrums!

Problem 1533

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

Problem 1532

Geometry Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle!

Problem 1531

Geometry Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord

Problem 1530

Geometry Problem 1530: Unlock the Secrets of Geometric Angles: Calculate the Measurement of an Angle in a Square and Rectangle Figure

Problem 1529

Geometry Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths

Thematic Poem:
Geometric Symphony: The Tale of a Square, a Circle, and Angle AMK

Within a square, so perfect and true,
A circle's grace, a geometric view,
With center O, it stands inscribed,
Touches sides with poise, in points described.

AB, BC, CD, AD, it meets with ease,
At E, F, G, and H, with gentle tease,
A symphony of shapes, in harmonious blend,
A dance of lines, that seem to never end.

The line BD, a path it takes,
Intersects the arc with calculated stakes,
At point K, where angles meet,
A junction formed, so sweetly neat.

AF and HK, two lines in play,
They intersect, in a wondrous way,
At point M, where paths converge,
A meeting point, a geometrical urge.

Now, angle AMK, the final quest,
A measure sought, a mathematical test,
With skill and wit, calculations made,
Solving the puzzle, with math displayed.

So, in this tale of squares and circles told,
A poetic ode to geometry bold,
With lines and points, and angles to see,
A mathematical journey, a captivating decree.

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

Search our site with Google: