SOLUTION: A circle having an area of 201 cm2 is cut into segments by a chord which is 3 cm from the center of the circle. Find the area of the smaller segment. A.75.93 sq. cm B.53.68 sq.

Question 1153289: A circle having an area of 201 cm2 is cut into segments by a chord which is 3 cm from the center of the circle. Find the area of the smaller segment.
A.75.93 sq. cm
B.53.68 sq. cm
C.18.98 sq. cm
D.38.65 sq. cm
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The area of the circle is 201 cm^2, and that gives a radius of 8 cm.
Draw this, making the chord parallel to the diameter. The distance to the chord is 3 cm and forms a right triangle with sides 3, 8 (the hypotenuse), so the other side, half the chord is sqrt(55) cm.
The central angle is cos ^(-1) 3/8 or 67.98 degrees, call it 68 degrees.
the area of the segment containing the chord and the two triangles formed by the perpendicular is 201*136/360 or 75.93 cm^2. But, the two triangles are not part of that area, for they are on the wrong side of the segment.
the area of each is 1/2 bh or 3 sqrt(55)/2, but both together make 3 sqrt(55)
subtract 3 sqrt(55) from the 75.93 to get 53.69 cm^2.
B

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