# Points #(5 ,4 )# and #(2 ,2 )# are #(5 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?

##### 3 Answers

the shortest arc happens to be

#### Explanation:

Given:

Angle subtended at the center is

The minor arc happens to be

The triangle formed by the two points and the center happens to be an isoceles triangle with the shortest angle formed at the center being

Remaining angle is

Angle at each of the vertex at the base is

Mid point happens to be

We calculate the radius of circle by pythagoras theorem in the right angled triangle formed by one of the point, say

Distance between one of the points, say

Also, the line joining

Consideing the ratio

Hence, the shortest arc happens to be

the shortest arc happens to be

Shortest Arc length

#### Explanation:

Since the center angle

Shortest length of the arc

**Shorter arc length between the points is** **unit.**

#### Explanation:

Angle subtended at the center by the arc is

Angle subtended at the center by the minor arc is

Distance between two points

Formula for the length of a chord is

where

subtended at the center by the chord.

Arc length is

Shorter arc length between the points is