Topics
Similarity
- Ratios of Areas of Two Triangles
- Basic Proportionality Theorem
- Property of an Angle Bisector of a Triangle
- Property of Three Parallel Lines and Their Transversals
- Similarity of Triangles (Corresponding Sides & Angles)
- Theorem of Areas of Similar Triangles
- Overview of Similarity
Pythagoras Theorem
- Pythagorean Triplet
- Property of 30°- 60°- 90° Triangle Theorem
- Property of 45°- 45°- 90° Triangle Theorem
- Theorem of Similarity in Right Angled Triangle
- Theorem of Geometric Mean
- Pythagoras Theorem
- Application of Pythagoras Theorem
- Apollonius Theorem
- Overview of Pythagoras Theorem
Circle
- Properties of Chords of a Circle
- Circles Passing Through One, Two, Three Points
- Secant and Tangent
- Tangent Theorem
- Tangent Segment Theorem
- Touching Circles
- Arc of the Circle
- Central Angle and the Measure of an Arc
- Congruence of Arcs
- Property of Sum of Measures of Arcs
- Inscribed Angle & Intercepted Arc
- Cyclic Quadrilateral
- Overview of Circle
- Theorem of Angle between Tangent and Secant
- Theorem of Internal Division of Chords
- Theorem of External Division of Chords
- Tangent Secant Segments Theorem
Geometric Constructions
- Construction of Similar Triangle
- Construction of a Tangent to a Circle at a Point on the Circle
- Construction of a Tangent to a Circle from a Point Outside the Circle
- Overview of Geometric Constructions
Co-ordinate Geometry
Trigonometry
Mensuration
Definition
Central Angle: An angle whose vertex is the centre of the circle is called a central angle.
Notes
Central Angle and the Measure of an Arc:
An angle whose vertex is the centre of the circle is called a central angle.
In the figure, ‘O’ is the vertex of the ∠AOB.
The ∠AOB in the figure is the central angle corresponding to arc AZB. The measure of the angle subtended at the centre by an arc is taken to be the measure of the arc.
1. The measure of a minor arc:
In the above figure, the measure of ∠AOQ = 70°.
∴ Measure of the minor arc AYQ is 70°.
It is written as m(arc AYQ) = 70°.
2. The measure of a major arc:
Measure of a major arc = 360° - measure of the corresponding minor arc
∴ Measure of major arc AXQ in the figure = 360° - 70° = 290°
3. The measure of a circle:
When the radius OA of a circle turns anti-clockwise, as shown in the above figure, through a complete angle, it turns through an angle that measures 360°. Its endpoint A completes one circle. The angle subtended at the center by the circle is 360°.
∴ The measure of the complete circle is 360°.
4. Measure of a semicircular arc:
The measure of a semicircular arc = 180°.
Shaalaa.com | Central Angles, Circle Arcs, Angle Measurement, Major Arcs vs Minor Arcs
Series: Central Angle and the Measure of an Arc
Related QuestionsVIEW ALL [5]
Find the central angle of the shaded sectors (each circle is divided into equal sectors).
| Sectors |  |
 |
 |
 |
| Central angle of each sector (θ°) |
