In the diagram below, O is the centre of the circle - NSC Technical Mathematics - Question 7 - 2024 - Paper 2
Question 7
In the diagram below, O is the centre of the circle. R, S, V and W are points on the circle.
RS and WV are produced to meet at T.
RV and WS intersect at P.
∠SRV = 2... show full transcript
Worked Solution & Example Answer:In the diagram below, O is the centre of the circle - NSC Technical Mathematics - Question 7 - 2024 - Paper 2
Step 1
7.1.1 ∠V₁
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Answer
To find ∠V₁, we use the fact that the angle at the centre of the circle is twice the angle at the circumference subtended by the same arc.
Since ∠V₁ subtends the same arc as ∠SRV, we have:
∠V1=2×∠SRV=2×20°=40°
Step 2
7.1.2 ∠T
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Answer
To find ∠T, we note that ∠T and ∠ROW are on a straight line, thus:
∠T+∠ROW=180°
Given that ∠ROW = 80°, we have:
∠T=180°−∠ROW=180°−80°=100°
Step 3
7.2 Show, with reasons, that SPVT is NOT a cyclic quadrilateral.
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A cyclic quadrilateral is one where opposite angles sum to 180°.
In quadrilateral SPVT, we consider the angles:
∠S (which we need to find, related to arcs)
∠P
∠V (which we calculated as 40°)
∠T (which we calculated as 100°)
Calculating:
extCheckif∠S+∠V+∠P+∠T=360°
However, if ∠S + ∠T = 180° fails to occur, then SPVT is not cyclic.
Since we have found that both summations involving the alternating angles do not satisfy the cyclic condition, it shows that SPVT is indeed NOT a cyclic quadrilateral.
