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## High school geometry

### Course: High school geometry > Unit 8

Lesson 13: Constructing a line tangent to a circle# Circles FAQ

Frequently asked questions about circles

## Why do we need to learn about circles?

There are many places where we use properties of circles in the real world. For example, architects often use arcs and sectors when designing buildings, and engineers use circles when designing gears and other mechanical parts. Additionally, understanding the properties of circles can help us solve problems in geometry, trigonometry, and calculus.

## What's the difference between a radius and a diameter?

The radius of a circle is the distance from the center of the circle to any point on the circle. The diameter is twice the radius, or the distance across the circle through the center.

## What are tangent and secant lines?

A tangent line is a line that touches a circle at just one point. A secant line is a line that cuts through a circle at two points.

## What are radians?

Radians are a unit of measurement for angles.

One radian is the angle measure that we turn to travel one radius length around the circumference of a circle.

We often use radians in geometry because they make working certain formulas easier.

## What is arc length?

Arc length is the distance along a curved line, like on the edge of a circle.

On a circle, we need to know the central angle of the arc left parenthesis, theta, right parenthesis and the radius of the circle left parenthesis, r, right parenthesis to find arc length.

If theta is in degrees:

If theta is in radians:

## What is a sector?

A sector is a part of a circle, defined by two radii (the plural of radius) and the arc between them. Think of it as "pie slice" of the circle.

## How do we find the area of a sector?

We need to know the central angle of the sector left parenthesis, theta, right parenthesis and the radius of the circle left parenthesis, r, right parenthesis to find the sector's area.

If theta is in degrees:

If theta is in radians:

Note that we could simplify the formula that uses radians a bit:

## What's an inscribed angle?

An inscribed angle is an angle that has its vertex on the circumference of a circle.

## What is an inscribed shape?

An inscribed shape is a shape that is drawn inside a circle such that all of its vertices are touching the circumference of the circle.

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