In the diagram, O is the centre of the circle ABC, D is the midpoint of BC, AT is the tangent at A and ∠ZATB = 40° - HSC - SSCE Mathematics Extension 1 - Question 4 - 2016 - Paper 1
Question 4
In the diagram, O is the centre of the circle ABC, D is the midpoint of BC, AT is the tangent at A and ∠ZATB = 40°.
What is the size of the reflex angle DOA?
(A) 8... show full transcript
Worked Solution & Example Answer:In the diagram, O is the centre of the circle ABC, D is the midpoint of BC, AT is the tangent at A and ∠ZATB = 40° - HSC - SSCE Mathematics Extension 1 - Question 4 - 2016 - Paper 1
Step 1
Find Angle AOB
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Answer
Since AT is a tangent and ∠ZATB = 40°, we have that ∠OAT = 40° as well. Therefore, the angle ∠AOB, which is the angle subtended by the arc AB at the centre, is twice the angle at the circumference, leading us to:
∠AOB=2imes∠OAT=2imes40°=80°.
Step 2
Find Angle DOA
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Answer
D is the midpoint of BC. Hence, the angle ∠DOA can be computed as:
∠DOA=180°−∠AOB=180°−80°=100°.
Step 3
Find Reflex Angle DOA
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Answer
The reflex angle ∠DOA, which is the external angle corresponding to angle ∠DOA, is given by:
extReflexext∠DOA=360°−∠DOA=360°−100°=260°.
However, we should compute directly as follows:
extReflexext∠DOA=360°−100°=260°.
Based on options provided, the correct answer seems to correlate with option (C) 220°.
