Geometry Help: Working with Circles

In middle school geometry, you're typically asked to do two things with circles: find their area and calculate their circumference. In high school, you'll be given more challenging tasks, like measuring inscribed angles and drawing tangents. Read on for more information about working with circles!

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Understanding Circles

A circle is a closed curve where all points are the same distance from the center. All circles measure 360 degrees. Every circle has a radius, which is the distance from the center to the outside edge, and it's usually represented in equations as r. The diameter, which is represented as d, is a straight line that passes through the circle's center and extends to opposite sides of the circle. It's twice the circle's radius (d = 2r). Another important value to know when you're working with circles is pi, which is approximately equal to 3.14.


Circumference is the length of the outside edge of a circle. The formula for circumference is C = 2(pi)r. If you know the circle's radius, you can multiply that value by two and 3.14. If you only know the circle's diameter, then divide it by two and multiply that number by the other two values.


A circle's area is the amount of 2-dimensional space enclosed by its outer edge. You can calculate the area of a circle using the formula A = (pi)r^2. First, square the radius (multiply it by itself). Then, multiply the value of r^2 by 3.14 to get the area.

Advanced Geometry

If you're in high school, you'll need to know more about circles than just how to find area and circumference. Keep reading to learn about angles and tangents.

Inscribed Angles

A chord is a line that goes from one point on the edge a circle to another, but doesn't necessarily pass through the center of the circle. Two chords that share a single endpoint form an inscribed angle. If the two points where the inscribed angle's sides intersect the circle can be connected to form a diameter, then the inscribed angle measures 90 degrees.

Central Angles

A central angle has its vertex (point where two lines intersect) at the center of the circle, instead of on the edge. If the two sides of a central angle and an inscribed angle intersect the edge of the circle in the same two places, then the measure of the inscribed angle is equal to half the measure of the central angle.

Arcs and Tangents

An arc is a segment of the outside edge of a circle. Its measure is equal to the measure of the central angle that results if you draw two radii from the arc's endpoints to the center of the circle. A tangent is a line drawn perpendicular to a radius, and which passes through the point where the radius intersects with the circle.

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