FORM THREE MATHEMTICS STUDY NOTES TOPIC 6:CIRCLES
Definition of Terms
Circle, Chord, Radius, Diameter, Circumference, Arc, Sector, Centre and Segment of a Circle
Define circle, chord, radius, diameter, circumference, arc, sector, centre and segment of a circle
A circle: is the locus or the set of all points equidistant from a fixed point called the center.
Arc: a curved line that is part of the circumference of a circle
Chord: a line segment within a circle that touches 2 points on the circle.
Circumference: The distance around the circle.
Diameter: The longest distance from one end of a circle to the other.
Origin: the center of the circle
Pi(π):A number, 3.141592…, equal to (the circumference) / (the diameter) of any circle.
Radius: distance from center of circle to any point on it.
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.
NB: Diameter = 2 x radius of circle
Circumference of Circle = PI x diameter = 2 PI x radius
A Tangent to a Circle
Describe a tangent to a circle
Tangent is a line which touches a circle. The point where the line touches the circle is called the point of contact. A tangent is perpendicular to the radius at the point of contact.
Tangent Properties of a Circle
Identify tangent properties of a circle
A tangent to a circle is perpendicular to the radius at the point of tangency. A common tangent is a line that is a tangent to each of two circles. A common external tangent does not intersect the segment that joins the centers of the circles. A common internal tangent intersects the segment that joins the centers of the circles.
Prove tangent theorems
Theorems Relating to Tangent to a Circle in Solving Problems
Apply theorems relating to tangent to a circle in solving problems
Two common tangents to a circle form a minor arc with a central angle of 140 degrees. Find the angle formed between the tangents.
Two tangents and two radii form a figure with 360°. If y is the angle formed between the tangents then y + 2(90) + 140° = 360°
The angle formed between tangents is 40 degrees.