PON is a diameter of the circle centred at O - NSC Mathematics - Question 8 - 2018 - Paper 2
Question 8
PON is a diameter of the circle centred at O. TM is a tangent to the circle at M, a point on the circle. R is another point on the circle such that OR || PM. NR and ... show full transcript
Worked Solution & Example Answer:PON is a diameter of the circle centred at O - NSC Mathematics - Question 8 - 2018 - Paper 2
Step 1
8.1.1 P̂
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Answer
Using the tangent chord theorem, the angle P̂ is equal to the angle at the circumference subtended by the same chord. Therefore,
P^=M^1=66°.
Step 2
8.1.2 M̂₂
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Answer
Since M̂₂ is an angle inscribed in a semicircle, it measures 90°. Thus,
M^2=90°.
Step 3
8.1.3 N̂₁
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Answer
The angle N̂₁ can be calculated as the sum of the angles P̂ and M̂₂:
N^1=180°−(90°+66°)=24°.
Step 4
8.1.4 Ō̂₂
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Answer
According to circle theorems, Ō̂₂ is equal to P̂:
Oˉ^2=P^=66°.
Step 5
8.1.5 N̂₂
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To find N̂₂, we can use the angles on a straight line:
