# Circles

High school geometry,

Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.

This course contains 14 segments:

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.

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.

Constructing regular polygons inscribed in circles

Have you ever wondered how people would draw a square, equilateral triangle or even hexagon before there were computers? Well, now you're going to do just that (ironically, with a computer). Using our virtual compass and straightedge, you'll construct several regular shapes (by inscribing them inside circles).

Constructing circumcircles & incircles

In our study of triangles, we spent a decent amount of time think about incenters (the intersections of the angle bisectors) and circumcenters (the intersections of the perpendicular bisectors). We'll now leverage this knowledge to actually construct circle inscribed and circumscribed about a triangle using only a compass and straightedge (actually virtual versions of them).

Constructing a line tangent to a circle

Learn how to construct tangents to circles with certain conditions using compass and straightedge. For example, draw the tangent to a given circle that passes through a given point.

Rating Not enough ratings 14 segments On Demand (Start anytime) Free Khan Academy On all desktop and mobile devices English Mathematics Math

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