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)#