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UPSC 2003: ‘A’ and ‘B’ are two fixed points in a field. A cyclist C moves such that ACB is always a right angle. In this context, which one of the following statements is correct?
(a)The path followed by the cyclist is an ellipse
(b)The path followed by the cyclist is a circle
(c)The path followed by the cyclist is an exponential curve
(d)This type of motion is not possible
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Not attemptedCorrect Answer: (b) The path followed by the cyclist is a circle
By Thales’ theorem, all points C lying on the circle with AB as diameter subtend a right angle at C (∠ACB = 90°). Thus the cyclist’s path is that circle, making option (b) correct; neither an ellipse nor an exponential curve preserves this condition, and the motion is perfectly feasible. ([engineeringtechnology.org](https://engineeringtechnology.org/engineering-graphics/geometry-review/thales-theorem/?utm_source=openai))
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Frequently Asked Questions
What is the correct answer to this UPSC 2003 Science & Technology question?▼
The correct answer is option (b): The path followed by the cyclist is a circle. Watch the detailed video explanation in our Sherlocking Prelims course on UnlockIAS.
Which year was this Quantitative Aptitude question asked in UPSC Prelims?▼
This question was asked in UPSC CSE Prelims 2003, GS Paper 1, as Question 141. It falls under Science & Technology > Quantitative Aptitude.
What is the difficulty level of this UPSC question?▼
This question is rated "moderate". It requires sound conceptual understanding of the topic.
How many UPSC Prelims questions have been asked from Quantitative Aptitude?▼
UPSC has asked 178 questions from Quantitative Aptitude (under Science & Technology) across multiple years. Visit the topic page to see the full list and year-wise trends.