# Circle Theorems mind map

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- Created by: connor27
- Created on: 25-11-15 19:25

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- Circle Theorems
- A tangent and a radius meet at 90 degrees.
- A tangent is a line that touches a single point on the circle.
- A tangent always makes a 90 degree angle where it meets the radius on the point where it touches the circumference

- If two lines of a triangle is the radius, then the triangle is isosceles.
- Because the radius is always the same these lines will be the same making it isosceles.
- In a question this will not appear with the ticks telling you that the lines are the same length

- The perpendicular bisector of a chord passes through the centre
- A chord is any line drawn across a circle. No matter where the chord is drawn the line that cuts it in half will go through the centre

- The angle at the centre of the circle is twice that of the angle at the circumference from the same two points
- The angle in a semicircle is 90 degrees
- A triangle drawn from two ends of the diameter will always form a 90 degree angle when it hits the circumference

- Angles in the same segment are equal
- All triangles drawn from a chord will have the same angle where they touch the circumference also the two angles on opposite sides of the chord add up to 180

- Angles opposite each other in a cyclic quadrilateral add up to 180
- A cyclic quadrilateral is a 4 sided shape where every corner touches the circumference

- Tangents from the same point are the same length
- Two tangents drawn from an outside point are the same length

- The alternate segment theorem
- The angle between a tangent and a chord is always equal to the angle in the opposite segment that is formed on the circumference by the two lines drawn from the chord

- A tangent and a radius meet at 90 degrees.

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