Asked by Cathy

Determine the area of the segment of a circle if the length of the chord is 15 inches & located 5 inches from the center of the circle.
Answered by Reiny
Make your sketch
let the radius be r
r^2 = 5^2 + 7.5^2 = 81.25
r - √81.25

central angle formed by the chord:
let Ø be the angle at the centre formed by the right-angled triangle

tanØ = 5/7.5
Ø = 33.69°
central angle is 2Ø = 67.38°

area of whole circle = π(√81.25)^2 = 81.25π

so by simple ratio:
area of <b>sector</b>:
sector/84=1.25π = 67.38/360
sector = ....

area of triangle formed by the chord in that sector
= (1/2)(15)(5) = 75/2

area of <b>segment</b> = 75/2 - area of sector

I will leave the button pushing up to you
Answered by Glen
42.35
Answered by Anonymous
89
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