Shape and Space 6
2 marks · HardA tangent touches a circle at point T. The chord AB passes through T. Given that angle ATB = 37°, write down the size of the angle in the alternate segment which is subtended by AB, and state which theorem you used.
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37°, alternate segment theorem
Also accept: 37°, by the alternate segment theorem; Angle = 37°, using the alternate segment theorem
Common mistakes: Incorrect theorem; Incorrect angle
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Marking points
M1 · 1 mark · Identifies and states use of the alternate segment theorem.
A1 · 1 mark · Correctly states the angle as 37°.
Worked solution
The angle in the alternate segment subtended by AB is 37° (by the alternate segment theorem).
The alternate segment theorem states that the angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment.