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CAT 2005 — QA Question 17

Basics of CirclesEasy

Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is

Answer & solution

Correct answer: 1 + π

  • A

    32

  • 1 + π

  • C

    4π3

  • D

    5

Solution

The ant will not go into the circles with centers B and C and radius = 1 m

The minimum distance that the ant has to traverse = the distance of the path A-H-G-D

HG = 1 m

AH = GD = 14 × Circumference of circle = π2

AH + GD = π m

∴ The ant must traverse (1 + π)m.

Hence, option (b).

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CAT 2005 QA Q17: Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of A — Solution | TheCATExam