There are more rules about a circle than you would expect. Learn them all though and you’ll be able to outfox the examiner.
A Tangent And A Radius Meet At 90°
A tangent is a line that touches one point on the circumference of the circle. The radius is just a straight line from the centre of the circle. When the two meet they always form a right angle.
Be careful though, they might not have the tick marks on the side like here. The examiner will expect you to know it’s an isosceles triangle, and that the two red angles marked are the same, just because two radii are involved.
The Perpendicular Bisector Of A Chord Passes Through The Centre Of A Circle
A chord is just a line drawn across a circle. Wherever it is though if you cut it in half with a perpendicular line, that line will go through the centre.
Angle At The Centre Is Twice The Angle At Circumference
From the same two points on a circle, the angle made at the centre will be twice that made at the circumference.
Angle In A Semicircle is Always 90°
Angles In The Same Segment Are Equal
Any triangles drawn from a chord will have the same angle where they touch the circumference.
Opposite Angles in A Cyclic Quadratic Add Up To 180°
In a four sided shape where every corner touches the circumference the opposite angles will add up to 180°.
Tangents From The Same Point Are The Same Length
Alternate Segments Are Equal
The angle between a tangent and a chord is equal to the angle in the opposite segment (that means the angle made at the circumference by two lines drawn from the chord).
Phew! OK this is pretty hard A* stuff. You will probably have to use a number of these rules to figure out some angles in a question. Ask your teacher for lots of examples.