Please can you explain all the circle theorem to me
Mathematics
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Answer
Circle theorems describe the relationships between angles, chords, tangents, and arcs in a circle.
- Angle at the center is twice the angle at the circumference: An angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the remaining part of the circle.
- Angles subtended by the same arc are equal: Angles subtended by the same arc at the circumference are equal.
- Angle in a semicircle is a right angle: The angle subtended by a diameter at any point on the circumference is a right angle (90°).
- Alternate Segment Theorem: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
- Opposite angles of a cyclic quadrilateral sum to 180°: In a cyclic quadrilateral (a quadrilateral with all four vertices on the circle), the sum of opposite angles is 180°.
- Angles in the same segment are equal: This is a restatement of theorem 2, emphasizing that points on the same arc form equal angles.
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