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Example: Find Angle Measure using Circle Theorems

 Post to:   Explanation:

Circle Circle illustration showing a radius, a diameter, the centre and the circumference

A circle is a simple shape of Euclidean geometry consisting of the set of points in a plane that is a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius.

## Terminology

A circle's diameter is the length of a line segment whose endpoints lie on the circle and which passes through the centre. This is the largest distance between any two points on the circle. The diameter of a circle is twice the radius, or distance from the centre to the circle's boundary. The terms "diameter" and "radius" also refer to the line segments which fit these descriptions. The circumference is the distance around the outside of a circle.

A chord is a line segment whose endpoints lie on the circle. A diameter is the longest chord in a circle. A tangent to a circle is a straight line that touches the circle at a single point, while a secant is an extended chord: a straight line cutting the circle at two points.

An arc of a circle is any connected part of the circle's circumference. A sector is a region bounded by two radii and an arc lying between the radii and a segment is a region bounded by a chord and an arc lying between the chord's end points.

http://en.wikipedia.org/wiki/Circle

(Our solved example in mathguru.com uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

·       Angles in the same segment of a circle are equal.

·       The sum of all the angles in a Triangle is 180 (Angle Sum Property)