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

Thematic Poem:
Geometry's Thrill: Conquering Bike Brainteasers

Riding on my bike one day,
A geometry problem came my way.
Tangent circles, angles unknown,
A brainteaser to call my own.

Two circles, O and Q they're named,
Tangent at C, as they're framed.
AB, the common tangent line,
Points A and B, they intertwine.

Angle OQB, a given clue,
Measuring 112, it's true.
But what of angle BAC,
A mystery that needs a crack?

I pondered, puzzled, scratched my head,
Geometry's riddles, I've always dreaded.
With compass, ruler, and my wits,
I tried to solve, bit by bit.

Lines, angles, and shapes, I traced,
Hoping the answer would be embraced.
Conundrums and puzzles, a math maze,
But I kept pedaling through the haze.

Geometry's realm, a challenge profound,
With circles and tangents all around.
But I pressed on, determined still,
To unlock the problem's hidden thrill.

With perseverance, I persevered,
Though my math skills were sometimes feared.
I scribbled, calculated, and guessed,
Eager to put my skills to the test.

And then, a spark of insight came,
A breakthrough in the problem's name.
Angles combined, equations revealed,
The answer, at last, was finally sealed.

A triumphant smile spread on my face,
As I solved the geometry case.
High school brainteaser, conquered with might,
I felt the thrill of math's delight.

So, to all the brainteasers out there,
With circles, lines, and angles to share,
I'll take on the challenge, without fear,
And solve the puzzles, year after year.