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

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.