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?

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Q: 141 (IAS/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?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,5,2,1,2,1

keywords: 

{'cyclist': [0, 0, 1, 0], 'ellipse': [0, 1, 0, 2], 'motion': [0, 0, 0, 3], 'exponential curve': [0, 0, 1, 0], 'circle': [0, 0, 2, 1], 'right angle': [0, 0, 1, 0], 'path': [1, 0, 4, 2], 'field': [1, 1, 4, 8]}

The question is concerned with the trajectory followed by a cyclist, such that points A, C, and B always form a right angle, where A and B are fixed points and C represents the cyclist`s position.

Option 1 suggests the path followed by the cyclist is an ellipse. This is incorrect as an ellipse would not consistently form right angles at the cyclist’s position.

Option 2, the correct answer, proposes that the path followed by the cyclist is a circle. If point C lies on the arc of a circle with diameter AB, then according to the properties of a circle, angle ACB would always be a right angle.

Option 3 offers an exponential curve as the cyclist`s path. This is incorrect as an exponential curve could not maintain a constant right angle with two fixed points.

Option 4 states that this type of motion is not possible. However, this is incorrect as the cyclist’s motion is entirely feasible if he maintains his position on a circular arc with diameter AB.