Shape and Space 6
2 marks · NormalState the alternate segment theorem and give an example of how it can be used to find an unknown angle in a circle.
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The angle between a tangent and a chord through the point of contact equals the angle in the alternate segment. Example: If the angle between the tangent and chord is 40°, the angle in the opposite segment is also 40°.
Common mistakes: Confusing with angle at centre theorem
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Marking points
B1 · 1 mark · States the alternate segment theorem correctly.
B2 · 1 mark · Gives a clear example of its use.
Worked solution
Alternate segment theorem: The angle between the tangent and the chord at the point of contact equals the angle in the alternate segment. For example, if the angle between the tangent and a chord is 40°, the angle in the opposite segment of the circle is also 40°.