What is shortest distance between the endpoints of the arc

Question

if arc AB has a length of 12π and represents three-fourths of the circumference of circle 0, what is the shortest distance between the endpoints of the arc?

Answer 1

Circumference = 2πr 

 

So, Arc AB = (3/4)(2πr) = 12π

 

                        (3/2)r = 12

 

                              r = 8

 

Central angle corresponding to major arc AB = (3/4)(2π) = 3π/2

 

So, central angle corresponding to minor arc AB = π/2 (a right angle).

 

Chord AB is the hypotenuse of a right triangle.  The legs of the right triangle are radii of the circle.

 

So, (AB)² = 8² + 8²    AB = √128 = 8√2