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GB-42-04-001 · Alternate segment theorem

ABC31.0°
Diagram not accurately drawn

AB is a chord of a circle. A tangent at A makes an acute angle of 31° with AB. C lies on the major arc AB, in the alternate segment for this tangent–chord angle. Find angle ACB and state the theorem used.

Circle Theorems: Alternate Segment Theorem Booklet p. 85 & p. 86
Method
Write each calculation beside the geometric reason that justifies it
Worked Example (GB-42-04-001)
1)
MathsReason
∠ACB=31∘\angle ACB=31^\circThe angle between a tangent and a chord equals the angle in the alternate segment.
Ans = 31°