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
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