Question

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 $\angle YOD = 30^\circ$. Which of the following correctly gives the relation among the three alternate paths from X to Y?

Accepted Answer

D. Radius $R = 2	ext{ m}$. $X$ is midpoint of $OA \implies OX = 1	ext{ m}$. $XADY = XA + 	ext{arc } AD + 	ext{arc } DY = 1 + \frac{2\pi(2)}{4} + \frac{30}{360} \cdot 2\pi(2) \approx 1 + 3.14 + 1.05 = 5.19	ext{ m}$. $XOBY = XO + OB + 	ext{arc } BY = 1 + 2 + \frac{60}{360} \cdot 2\pi(2) \approx 3 + 2.09 = 5.09	ext{ m}$. $XODY = XO + OD + 	ext{arc } DY = 1 + 2 + \frac{30}{360} \cdot 2\pi(2) \approx 3 + 1.05 = 4.04	ext{ m}$. Ratio $XADY : XOBY : XODY :: 5.19 : 5.09 : 4.04$.

Geometry: Paths in Circular Field

Explanation

Practise this under exam conditions