Question 1135825
Calculate the area of the major segment of a circle of radius 10cm cut off by a chord of length 12cm
<pre>Area of triangle formed by the 2 radii and the chord: 48 cm<sup>2</sup>
Area of non-right triangle is also: {{{matrix(1,6, (1/2)(10)(10), "*", sine, of, central, angle)}}} ====> 48 = 50 sin of central angle
{{{matrix(1,3, 48/50, or, 24/25)}}} = sin of central angle
{{{matrix(1,4, sin^(- 1) (24/25), "=", Central, angle)}}}
73.74<sup>o</sup> = Central angle (smaller segment's angle) 
Larger segment’s ∡: 286.26<sup>o</sup> (360<sup>o</sup> - 73.74<sup>o</sup>)
{{{highlight_green(system(matrix(1,6, Area, of, "circle:", pi * r^2, or, 100pi), matrix(1,10, Area, of, larger, "segment:", (286.26/360) * 100pi, "=", 79.517pi, or, 249.81, cm^2)))}}}
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?