# Geometry Problem 1528: Cracking the Circle Code: Unveiling the Tangent and
Angle of an Inscribed Circle within a 90-Degree Circular Sector. Difficulty Level: High School.

A circle with center Q is inscribed in a circular sector AOB with a 90-degree angle and center O. The circle is tangent to OB at point E. Find the measure of angle QFE.

## Discover Even More: See Also...

### Problem 1529

### Problem 1527

### Problem 1526

### Problem 1525

### Problem 1524

### Problem 1523

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Thematic Poem:

Unlocking the Circle's Hidden Code

Within a circle's bounds we seek,

To find the
hidden code unique.

A tangent and an angle rare,

Within a sector, we'll find them there.

With careful measure and calculation,

We'll unlock
this circle's foundation.

For in its inscribed form
we see,

A world of geometry.

The tangent line, it touches close,

A point of
contact we disclose.

And from that point, we measure
true,

The angle that we seek anew.

Within this ninety-degree space,

We find the
circle's hidden grace.

Its tangents and angles now
revealed,

A treasure trove that's unconcealed.

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

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