Question

A circle has a chord that goes from `( 3 pi)/2` to `(7 pi) / 4` radians on the circle. If the area of the circle is `121 pi`, what is the length of the chord?

Answer 1

See geometric figure:
Chord, `bar(AB) = 11sqrt(2)`

Explanation:

This straight forward problem:
A) Determiner the radius from `C_A=piR^2`; `R =11`
Look at the angular displacement between `A ->B` it form
a right angle at the center so trangle AOB is an "isosceles right angle". Thus the ratio of side of an isosceles right triangle is:
`s_1:s_2:h=1:1:sqrt(2)` So for triangle AOD`=> a:f:bar(AD)=1:1:sqrt(2)`
`AD=11sqrt(2)/2`, thus the chord, `AB=11sqrt(2)`