Circles theorem
Circle Theorems
1. Alternate Segment Theorem
The angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment.
2. Angle at the Centre Theorem
The angle at the center is twice the angle at the circumference when both angles subtend the same arc.
3. Angles in the Same Segment Theorem
Angles in the same segment are equal.
4. Angles in a Semicircle
The angle in a semicircle is 90 degrees (a right angle).
5. Chord of a Circle
The perpendicular from the center of a circle to a chord bisects the chord (splits the chord into two equal parts).
6. Cyclic Quadrilateral
The opposite angles in a cyclic quadrilateral are supplementary (they add up to 180°).
7. Tangent of a Circle
Two important properties of tangents:
- The angle between a tangent and a radius at the point of contact is 90 degrees (a right angle).
- Tangents drawn from an external point are equal in length.
These theorems form the foundation of circle geometry and are crucial for solving various problems related to circles in mathematics.
Quiz 1
