A chord with a length of 6 runs from pi/12 to pi/2 radians on a circle. What is the area of the circle?

2 Answers
Jan 17, 2018

Area of the circle is 30.3 sq.unit.

Explanation:

Formula for the length of a chord is L_c= 2r sin (theta/2)

where r is the radius of the circle and theta is the angle

subtended at the center by the chord.

theta= pi/2-pi/12 = 90-15=75^0

:. L_c= 2 * r * sin (theta/2) ; L_c=6 , theta=75^0 unit or

r= 6/(2 * sin 37.5) =3/sin 37.5~~4.93 unit.

Area of the circle is A_c=pi*r^2= pi*4.93^2~~76.30(2dp)

sq.unit [Ans]

Jan 17, 2018

Area of circle A_c ~~ color(purple)(76.2942)

Explanation:

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Chord length AB =Ch = 2 * r * sin (theta/2) where theta is /_(AOM)

theta = /_(AOM) = theta = (pi/2) - (pi/12) = (5pi)/12

theta / 2 = ((5pi)/12) / 2 = (5pi)/24

Given Chord length AB = Ch = 6

r = 6 / (2 * sin ((5pi)/24) ~~color(blue)(4.928)

Area of the circle A_c = pi r^2 = pi * (4.928)^2

Area of circle A_c ~~ color(purple)(76.2942)