Shape and Space 6
3 marks · NormalIn the diagram, O is the centre of the circle. AB is a tangent to the circle at A. OC is a diameter. OA and OB are radii, and angle OAB = 28°.
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The angle between the tangent and the chord at A (angle OAB) is equal to the angle in the alternate segment (angle ACB), so angle ACB = 28°.
Must show: alternate segment angle
Common mistakes: Using angle at centre instead of alternate segment theorem
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Identifies application of alternate segment theorem.
M2 · 1 mark · Relates angle OAB to angle in opposite segment.
A1 · 1 mark · States angle ACB = 28°.
Worked solution
By the alternate segment theorem, the angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment. Therefore, angle ACB = angle OAB = 28°.