Circle Theorems

• A tangent is a straight line that touches a circle at one point only.
• Circle Theorem 1 is that the angle at the centre is double the angle at the circumference when bounded by the same arc
• Circle Theorem 2 is the angle at the circumference formed by a semicircle is always a right angle.
• Circle Theorem 3 is angles at the circumference by the same arc are equal.
• Circle Theorem 4 is a cyclic quadrilateral with four vertices on the circumference, where the opposite angles are supplementary.
• Circle Theorem 5 is when the radius is perpendicular to the tangent at a point of contact on the circumference, creating a 90 degree angle
• Circle Theorem 6 (Alternate Segment Theorem) is the angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment
• a sector is the area between 2 radii and an arc
• an arc is a portion of the circumference
• a radius extends from the centre of a circle to the circumference
• a chord extends from one side of the circle to the other, however does not pass through the centre
• a segment is the area between a chord and an arc