10 – Rule 9

Alternate segment theorem 2:

Another example of the alternate segment theorem

Prove that the angle between the tangent and the chord (s) is equal to the angle in the alternate segment (q).

Line OA is at 90° to the tangent

Angle OAC is 90° – s

Triangle AOC is isosceles with two radii sides

So angle ACO is also 90° – s

Therefore AOC is 180 – (90° – s) – (90° – s) = 2s

Angle at centre is twice angle at circumference means angle q is half AOC or s

Hence q = s

Your Turn:

Find the angle q:

Enter your answer here:

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