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

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