MBApyq

Geometry: Paths in Circular Field

XAT 2010 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

All XAT 2010 questionsMore Quantitative Ability questionsAll XAT QADI

In a circular field, AOB and COD are two mutually perpendicular diameters having length of 4 meters. X is the mid - point of OA. Y is the point on the circumference such that ∠YOD=30∘\angle YOD = 30^\circ. Which of the following correctly gives the relation among the three alternate paths from X to Y?

  1. A.

    XOBY : XODY : XADY :: 5.15 : 4.50 : 5.06

  2. B.

    XADY : XODY : XOBY :: 6.25 : 5.34 : 4.24

  3. C.

    XODY : XOBY : XADY :: 4.04 : 5.35 : 5.25

  4. D.

    XADY : XOBY : XODY :: 5.19 : 5.09 : 4.04

  5. E.

    XOBY : XADY : XODY :: 5.06 : 5.15 : 4.50

Answer

D

Explanation

Radius R=2 mR = 2\text{ m}. XX is midpoint of OA  ⟹  OX=1 mOA \implies OX = 1\text{ m}. XADY=XA+arc AD+arc DY=1+2π(2)4+30360⋅2π(2)≈1+3.14+1.05=5.19 mXADY = XA + \text{arc } AD + \text{arc } DY = 1 + \frac{2\pi(2)}{4} + \frac{30}{360} \cdot 2\pi(2) \approx 1 + 3.14 + 1.05 = 5.19\text{ m}. XOBY=XO+OB+arc BY=1+2+60360⋅2π(2)≈3+2.09=5.09 mXOBY = XO + OB + \text{arc } BY = 1 + 2 + \frac{60}{360} \cdot 2\pi(2) \approx 3 + 2.09 = 5.09\text{ m}. XODY=XO+OD+arc DY=1+2+30360⋅2π(2)≈3+1.05=4.04 mXODY = XO + OD + \text{arc } DY = 1 + 2 + \frac{30}{360} \cdot 2\pi(2) \approx 3 + 1.05 = 4.04\text{ m}. Ratio XADY:XOBY:XODY::5.19:5.09:4.04XADY : XOBY : XODY :: 5.19 : 5.09 : 4.04.

Related Quantitative Ability questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace