Circles & angles & arcs

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1. Central angle

A central angle is an angle whose vertex is the center of the circle.

Example: xOy is a central angle , and it intercepts at arc AB

If you want to find the measure of the arc AB it is equal to the angle AOB

Example: AOB=50 degrees then the arc AB=50 degrees

2. Inscribed Angle

An inscribed angle is an angle whose vertex is on the circle and whose sides are chords of the circle. There are 2 types of inscribed angle:

a. If you want the measure of the arc it intersepts it is equal to the arc divided by 2 Example (fig1):angle ZAT=arc FE divided 2

b. Angle formed by a tangent and a chord intersecting at a point on the circle if you want the measure of the arc it intercepts it is equal to the arc divided by 2.

Example: (fig2): angles ATX, BTX, and ETY are inscribed angles

Big image
Big image

3. Exterior angles

An exterior angle is an angle whose vertex outside the circle and its sides cut the circle.There are 3 types of exterior angles: