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
Since O is the center of the circle, the angle at the center is twice the angle at the circumference subtended by the same arc. Therefore, we have:
∠V1=2×∠SRV=2×20°=40°
Hence, ∠V1 = 40°.
Step 2
7.1.2 ∠T
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Answer
Since RS and WV are straight lines, the angles on a straight line sum to 180°. We already have:
∠SRV=20°∠T=180°−∠V1
Substituting for ∠V1:
∠T=180°−40°=140°
Thus, ∠T = 140°.
Step 3
7.2 Show, with reasons, that SPVT is NOT a cyclic quadrilateral.
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Answer
For SPVT to be a cyclic quadrilateral, the opposite angles must be supplementary. We check the angles:
∠S+∠P=140°+40°=180°∠T+∠V=180°
However,
extAngle(∠S+∠T)=140°+20°=160° which is not supplementary to 180°.
Hence, SPVT is NOT a cyclic quadrilateral as it's not satisfying the cyclic condition.
