What Are The 8 Circle Theorems?
Students will memorise all of the circle theorems and then practing applying that knowledge to a set of questions. It's important that you have a firm grasp of angles on parallel lines before you move on to circle theorems. You will also have to remember that angles on a straight line and angles in any triangle equal to 180 degrees, and that angles about a point equal to 360 degrees.
The graphic above shows 6 circle theorems. 1) The angle at the center is twice the angle at the circumference. 2) Angles in the same segment are equal. 3) Opposite angles in a cyclic quadrilateral are equal. 4) The angle in a semi-circle is always 90°. 5) The alternate angle theorem. 6) The angle between the tangent and the radius is always 90°.
Circle Theorems Question 1
Circle Theorems Question 2
The angle at the center is twice the angle at the circumference so x equals 132°.
Circle Theorems Question 3
The triangle formed when the radius meets the circumference is isosceles, so a equals 30°. The third angle in the triangle is 120° because angles in a triangle equal 180°. b equals 240° because angles around a point equal 360°.