A path consists of two segments

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

A path consists of two segments. Segment 1: the line from

(0,0)

(2,1)

. Segment 2: the quarter–circle of radius

1

centered at

(2,1)

from

(2,1)

(3,0)

in the clockwise direction. What is the total length of the path? (a)

\sqrt{5}+\sqrt{2}

(b)

\sqrt{5}+\pi

(c)

\sqrt{5}+\dfrac{\pi}{2}

(d)

\sqrt{5}+\dfrac{\pi\sqrt{2}}{2}