November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Circles: arcs, chords, tangents, sector.

In this section, you’ll learn more parts to the circles; say an arc- major and minor, sector, segment, secant and tangent. It will be done with the help of some examples, practice questions with solution, using multimedia explanation by the instructor and own handwriting.

An arc is a part of the circumference of a circle. The longer arc is called the major arc while the shorter one is called the minor arc. Arc is measured in degrees and length. If the measure of minor arc is ?i.e. the measure of the central angle intercepted by the arc, then the measure of major arc is (360° - ). E.g. if measure of a minor arc is 100°, then major arc is (360° – 100°) = 260°. Now let us look at the relationship of radius and measure of central angle: if r is the radius of the circle and is the measure of central angle, then length of the arc intercepted by the angle ?is given by /360° × 2?r. E.g. = 120°, then length of the intercepted arc is 4?/3 units.

To remember-basic terms related to circle:

In this section, you’ll learn more parts to the circles; say an arc- major and minor, sector, segment, secant and tangent. It will be done with the help of some examples, practice questions with solution, using multimedia explanation by the instructor and own handwriting.

An arc is a part of the circumference of a circle. The longer arc is called the major arc while the shorter one is called the minor arc. Arc is measured in degrees and length. If the measure of minor arc is ?i.e. the measure of the central angle intercepted by the arc, then the measure of major arc is (360° - ). E.g. if measure of a minor arc is 100°, then major arc is (360° – 100°) = 260°. Now let us look at the relationship of radius and measure of central angle: if r is the radius of the circle and is the measure of central angle, then length of the arc intercepted by the angle ?is given by /360° × 2?r. E.g. = 120°, then length of the intercepted arc is 4?/3 units.

To remember-basic terms related to circle:

- A chord is a straight line joining two points on the circumference. The longest chord is the diameter and diameter passes through the center. E.g.
*A*and*B*are the points on the circle. When we join these two points,*AB*is the chord. - A sector is a region enclosed by two radii and an arc. In a circle with center at
*O*and*A*,*B*two points on the circumference,*AOB*is the angle subtended by the arc*AB*at the centre*O*. The larger region is called the major sector and the smaller one, a minor sector. - A segment of a circle is the region enclosed by a chord and an arc of the circle. The larger segment is the major segment and the smaller one, the minor segment.
- A secant is a line intersecting the circle at two distinct points. If point
*A*and*B*are outside the circle and we join these, it intersects circle at two distinct points. - If a line and a circle have only one intersection point, this line is called a tangent. It is always perpendicular to the radius drawn to the point of intersection. This property is abbreviated as tan rad.
- The diameter of a circle divides the circle into equal halves and each part is called a semi circle.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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