Circle Theorems

Question 1

State all of the circle theorems.

Answer 1

• A radius bisects a chord at 90º.
• A tangent and radius will meet at 90º.
• Two external tangents meeting are equal in length.
• Angle at the centre of a circle is twice the angle at its circumference.
• Angles (subtended) in the same segment are equal (bow tie theorem).
• Angle in a semi-circle = 90º.
• Opposite angles in a cyclic quadrilateral add up to 180º.
• Alternate segment theorem: the angle between a chord and and a tangent = the angle on the circumference on the opposite segment as that of the chord and tangent.