Asked by Cassandra
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?
Answers
Answered by
Steve
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
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
Answered by
Devin
@steve is completely correct!
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