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.

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.

Geometry Problems

Open Problems

Visual Index

All Problems

Square

Triangle

Circle

Diameter & Chord

Semicircle

Angle

Circle Tangent Line

Perpendicular lines

Right Triangle

Special Right Triangle

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