# Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle! - A High School Challenge

Given a square ABCD with the inner semicircle of diameter AD, line segment CT is tangent to the semicircle at point T. Find the measure of angle CTD.

### Thematic Poem: Unraveling the Mystery of Geometry Problem 1532

Amidst the realm of angles and shapes,
Lies a mystery that's hard to break,
A problem that beckons the curious mind,
To find the angle that's so hard to define.

In a square with a semicircle true,
With point T that's tangential too,
A quest begins to crack the code,
And find the measure of CTD to behold.

Special right triangle, tangency point,
A puzzle that's no mere easy joint,
But fear not, dear seeker, for you shall find,
The answer that's been hidden in plain sight.

So take up your tools and let your mind soar,
For the challenge that lies ahead is one to adore,
And as you delve deep into geometry's core,
The mystery shall be unlocked forevermore.

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