UPSC Prelims 2003 · General Studies

Question 141: Basic Numeracy

‘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?

aThe path followed by the cyclist is an ellipse

bThe path followed by the cyclist is a circle

cThe path followed by the cyclist is an exponential curve

dThis type of motion is not possible

AnswerThe answer is (b).

An angle in a semicircle is a right angle (Thales' theorem). If C moves so that angle ACB is always 90 degrees, C lies on the circle with AB as its diameter. So the cyclist's path is a circle (excluding the points A and B themselves). An ellipse would need a constant sum of distances to two points, not a constant angle.

Why each option is right or wrong

(a) An ellipse is the locus of a constant sum of distances from two points, not of a right angle.
(b) Correct: a circle with AB as diameter.
(c) An exponential curve has no link to a fixed right angle over AB.
(d) The motion is possible: C can move round the circle.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2003, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.