Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long? I don't even understand how to start a question like this?

Answer 1

As usual, draw a diagram. Half the chord is of length 4. Draw the radius through the chord's center. Now you have a right triangle with leg 4 and hypotenuse 8, which subtends an angle x such that

sinx = 1/2
So, x = 30 degrees.
The whole chord thus subtends an angle of 60 degrees.

The area of a circular sector of angle x is 1/2 r^2 x, or in this case, 32π/3

The area of the triangle is 16√3

So, the smaller segment cut by the chord has area 32π/3-16√3

Answer 2

@steve is completely correct!