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
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:
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.
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
When two chords intersect inside a circle like above then:
