Asked by kenzi
in circle p, chord cd is 12 inches long and measure of arc cd=90°, find the exact area of the segment bounded by chord cd and arc cd.
Answers
Answered by
Reiny
arc cd=90° ??
this makes no sense, since arc length is measured in linear units , not degrees
Are you saying that the arc cd subtends a 90° angle at the centre?
If so,
then r^2 + r^2 = 12^2
2r^2 = 144
r^2 = 72
r = 6√2
area of whole circle = 72π inches^2
area of 1/4 = 18π
area of triangle with 12 as the hypotenuse
= (1/2)(√72)(√72) = 36
area of segment = 18π - 36 inches^2
or appr 20.55 inches^2
this makes no sense, since arc length is measured in linear units , not degrees
Are you saying that the arc cd subtends a 90° angle at the centre?
If so,
then r^2 + r^2 = 12^2
2r^2 = 144
r^2 = 72
r = 6√2
area of whole circle = 72π inches^2
area of 1/4 = 18π
area of triangle with 12 as the hypotenuse
= (1/2)(√72)(√72) = 36
area of segment = 18π - 36 inches^2
or appr 20.55 inches^2
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