This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Measuring Circles.

In this section you'll learn, basics and formulas for measuring circles, using explanation and examples. You know from earlier learnings that the circumference of a circle is given by:

*C* = 2?*r*

Now we walk through ways to measure angle in degrees and in radians for a circle. A degree is defined as 1/360 of a rotation of a radius about the center of a circle. Simply put, a circle is divided into 360 equal degrees, and a right angle (1/4th of the rotation) is 90°. It also gives the geometric definition of radians based on measuring distances, which states that the measure in radians is determined by the intersected arc length (*s*) divided by radius (*r*). It can be expressed as,

(radians) = arc length/radius =*s*/*r*

For example, 0.84 radians when converted to degrees, it comes to 48.13°.

To remember- formulas for working with angles in circles:

In this section you'll learn, basics and formulas for measuring circles, using explanation and examples. You know from earlier learnings that the circumference of a circle is given by:

Now we walk through ways to measure angle in degrees and in radians for a circle. A degree is defined as 1/360 of a rotation of a radius about the center of a circle. Simply put, a circle is divided into 360 equal degrees, and a right angle (1/4th of the rotation) is 90°. It also gives the geometric definition of radians based on measuring distances, which states that the measure in radians is determined by the intersected arc length (

(radians) = arc length/radius =

For example, 0.84 radians when converted to degrees, it comes to 48.13°.

To remember- formulas for working with angles in circles:

- Central Angle: A central angle is an angle formed by two intersecting radii such that its vertex is at the center of the circle.
- Inscribed Angle: An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
- Tangent Chord Angle: An angle formed by an intersecting tangent and chord has its vertex "on" the circle.
- Angle Formed Inside of a Circle by Two Intersecting Chords: When two chords intersect "inside" a circle, four angles are formed. At the point of intersection, two sets of vertical angles formed are equal.
- Angle Formed Outside of a Circle by the Intersection of, "Two Tangents" or "Two Secants" or "a Tangent and a Secant": Angle formed outside is equal to half the difference of intercepted arcs.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

- Mathematics > General
- Mathematics > Geometry
- Education > General

- Grade 9
- Grade 10
- Grade 11
- Grade 12

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Prove that all circles are similar.