SOLUTION: Calculate the area of the major segment of a circle of radius 10cm cut off by a chord of length 12cm

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Question 1135825: Calculate the area of the major segment of a circle of radius 10cm cut off by a chord of length 12cm
Found 3 solutions by greenestamps, MathLover1, MathTherapy:
Answer by greenestamps(13203) About Me  (Show Source):
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Draw the radii to the two ends of the chord, and draw the radius that is perpendicular to the chord.

The radius perpendicular to the chord bisects the chord. Your picture now has two right triangles with hypotenuse 10 and one leg 6; the other leg (distance from center of circle to chord) is then 8.

Use those right triangles to determine the central angle corresponding to the chord; the central angle of the major segment of the circle is 360 degrees minus that angle.

Multiply the area of the whole circle by the fraction of 360 degrees represented by the central angle of the major segment of the circle.

Answer by MathLover1(20850) About Me  (Show Source):
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first find the angle subtended at the center by the chord, we will have to use the Cosine Rule
A=cos%5E-1%28%28b%5E2%2Bc%5E2-a%5E2%29%2F2bc%29
b=c=radius=10cm
a=chord_+length=12cm
A=angle subtended at center of circle

+A=cos%5E-1%28%2810%5E2%2B10%5E2-12%5E2%29%2F%282%2A10%2A10%29%29
A=cos%5E-1%28%28100%2B100-144%29%2F200%29
A=cos%5E-1%2856%2F200%29
A=cos%5E-1%280.28%29
A=73.74°


Area=%281%2F2%29%2Ar%5E2%28%282pi%2AA%29%2F360-sin%28A%29%29
Area=%281%2F2%29%2A10%5E2%28%282%2A3.14%2A73.74%29%2F360-sin%2873.74%29%29
Area=%281%2F2%29%2A100%281.2863533-0.960001%29
Area=%281%2F2%29%2A32.63523
Area=16.32cm%5E2

Answer by MathTherapy(10555) About Me  (Show Source):
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Calculate the area of the major segment of a circle of radius 10cm cut off by a chord of length 12cm
Area of triangle formed by the 2 radii and the chord: 48 cm2

Area of non-right triangle is also:  ====> 48 = 50 sin of central angle

matrix%281%2C3%2C+48%2F50%2C+or%2C+24%2F25%29 = sin of central angle

matrix%281%2C4%2C+sin%5E%28-+1%29+%2824%2F25%29%2C+%22=%22%2C+Central%2C+angle%29

73.74o = Central angle (smaller segment's angle) 

Larger segment’s ∡: 286.26o (360o - 73.74o)



The other person's answer is NOWHERE close to being correct. How can the area of the larger segment be a little more than 16 cm^2 when the area of the smaller segment

is a little more than the area of the triangle formed by the 2 radii and the chord (48 cm^2)? Can't these people see how RIDICULOUS and NONSENSICAL their answers are?