Points (3 ,2 ) and (7 ,4 ) are ( pi)/3 radians apart on a circle. What is the shortest arc length between the points?

1 Answer
Mar 5, 2016

4.68 unit

Explanation:

Since the arc whose end points are (3,2) and (7,4) ,subtends anglepi/3 at the centre,the length of line joining these two points will be equal to its radius.
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Hence length of radius r= sqrt((7-3)^2+(4-2)^2)=sqrt20=2sqrt5

nowS/r= theta=pi/3,where s= arc length and r= radius,theta =angle subtended be arc at the centre.
S=pi/3*r=3.14/3*2sqrt5=4.68unit