# Circle

definition: A circle is a simple shape, consisting of those points in a plane that are a given distance from a given point, the centre.

• origin: the center of the circle
• radius: the distance from the center of a circle to any point on it.
• diameter: the longest distance from one end of a circle to the other. Diamter = 2.radius
• circumference: the distance around the circle.
• π - pi: number equal to 3.141592..., that is (the circumference) / (the diameter) of any circle.
• arc: a curved line that is part of the circumference of a circle. The arc of a circle is measured in degrees. The whole arc of the circle is 360°
• chord: a line segment within a circle that touches 2 points on the circle.
• sector: is like a slice of pie (a circle wedge).
• tangent of circle: a line perpendicular to the radius that touches ONLY one point on the circle.

Circumference of circle = π.diameter = 2.π.radius

Area of circle = π.radius2 Radius is noted with r, diameter with d and circumference with P

P = π.d = 2.π.r
A = π.r2

Area of circle sector K: (with central angle θ and radius r )
if the angle θ is in degrees, then area = (θ/360) π r2
if the angle θ is in radians, then area = (θ/2) r2

### How do we find a central angle?

If we would like to find a central angle θ by given arc length(l) we use the formula:

θ = 360.l/P = (360.l)/(2πr) = (180.l)/(πr)

### Inscribed angle

An inscribed angle is an angle with its vertex on a circle and with sides that contain chords of the circle.
At the picture angle APB is inscribed angle.

The measure of an inscribed angle is equal to one-half the degree measure of its intercepted arc.

### Angles between two chords

When two secants intersect inside a circle, the measure of each angle formed is half the sum of the measures of the intercepted arcs. In the figure, arc AB and arc CD are relevant 60° and 50° so the measures of angle 1 and 2 is (60° + 50°)1/2

Sometimes, secants intersect outside of circles. When this happens, the measure of the angle formed is equal to half the difference of the degree measures of the intercepted arcs.

When two chords intersect inside a circle like above then:

AE.EC = DE.EB

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