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

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)   (Show Source): You can put this solution on YOUR website!

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)   (Show Source): You can put this solution on YOUR website!

first find the angle subtended at the center by the chord, we will have to use the Cosine Rule

=angle subtended at center of circle

°

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
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
= sin of central angle

73.74^o = Central angle (smaller segment's angle)
Larger segment’s ∡: 286.26^o (360^o - 73.74^o)

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?
RELATED QUESTIONS
A crossection of a tunnel is in the shape of a major segment of a circle of radius 1m on... (answered by ankor@dixie-net.com)
1. calculate the angle at the centre of a circle ,subtended by a chord 6cm from the... (answered by solver91311)
calculate the angle at the centre of a circle subtended by a chord 6cm from the centre of (answered by Alan3354)
Find the area of a segment formed by a chord 8" long in a circle with radius of... (answered by ikleyn)
AB is a chord of a circle of radius 10cm, M is the midpoint of AB and line NM cut AB.... (answered by greenestamps)
Express the length L of a chord of a circle with radius 10cm as a function of the... (answered by Edwin McCravy)
The distance of a chord of a circle of radius is 4cm. Calculate the length of the... (answered by ikleyn,math_tutor2020)
An equilateral triangle is inscribed in a circle with a radius of 6". Find the area of... (answered by edjones)
Prove that the area of the minor segment cut off from a circle of radius r cm by a chord... (answered by Alan3354)