The points A, B, C and D lie on a circle and the tangents at A and B meet at T, as shown in the diagram - HSC - SSCE Mathematics Extension 1 - Question 3 - 2017 - Paper 1
Question 3
The points A, B, C and D lie on a circle and the tangents at A and B meet at T, as shown in the diagram.
The angles BDA and BCD are 65° and 110° respectively.
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Worked Solution & Example Answer:The points A, B, C and D lie on a circle and the tangents at A and B meet at T, as shown in the diagram - HSC - SSCE Mathematics Extension 1 - Question 3 - 2017 - Paper 1
Step 1
Calculate ∠ABD
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Answer
Since angle BDA is given as 65°, ∠ABD can also be calculated as:
∠ABD=∠BDA=65°
Step 2
Calculate ∠BCD
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Answer
We are given that angle BCD is 110°. Hence, we can denote this directly:
∠BCD=110°
Step 3
Use the property of angles in a circle
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Answer
According to the inscribed angle theorem, the angle subtended at the center (angle TAD) is double the angle at the circumference (angle BCD). Therefore:
∠TAD=2imes∠BCD=2imes110°=220°
Step 4
Correct the angle for exterior angles
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Answer
Since angles are measured within 0° to 360°, the applicable angle here is the supplementary angle to match the context:
∠TAD=360°−220°=140°
Step 5
Final adjustment to match options
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Answer
To find the correct representation for the options, we find:
