# Geometry

We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
Community Questions

# Circles

Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.
Community Questions
All content in “Circles”

## Circle basics

Make sure you're familiar with notation and key terms like radius, diameter, circumference, pi, tangent, secant, and major/minor arcs before you dive into the rest of the circles content.

## Arc measure

Arc measure is equal to the arc's central angle. We'll explore this fact and solve some problems related to it.

## Arc length (degrees)

Think about the relationship between central angle and arc length. This tutorial uses degrees not radians.

Most people know that you can measure angles with degrees, but only exceptionally worldly people know that radians can be an exciting alternative. As you'll see, degrees are somewhat arbitrary.

Think about the relationships between arc measures, central angles, and arc length in radians.

## Sectors

Learn how to find the area of a sector.

## Inscribed angles

We'll now dig a bit deeper in our understanding of circles by looking at inscribed angles and related properties.

## Inscribed shapes problem solving

Use properties of inscribed angles to prove properties of inscribed shapes, then apply these properties some fun problem solving!

## Properties of tangents

Explore, prove, and apply properties of circles that involve tangents.

## Area of inscribed triangle

This more advanced (and very optional) tutorial is fun to look at for enrichment. It builds to figuring out the formula for the area of a triangle inscribed in a circle!

## Standard equation of a circle

Learn about the standard form to represent a circle with an equation. For example, the equation (x-1)^2+(y+2)^2=9 is a circle whose center is (1,-2) and radius is 3.

## Expanded equation of a circle

Learn how to analyze an equation of a circle that is not given in the standard form. For example, find the center of the circle whose equation is x^2+y^2+4x-5=0.