A chord with a length of #3 # runs from #pi/12 # to #pi/2 # radians on a circle. What is the area of the circle?

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Answer 1 · 2017-08-23T12:08:31

Area of the circle is #19.07# sq.unit.

Chord length #L= 3 # unit

Angle subtended at center by the chord is

#c= (pi/2-pi/12)= 90-15=75^0#

We know chord length #L = 2r sin (c/2) ;r# is radius .

#:. 3 =2*r* sin (75/2) :. r = 3/ (2*sin37.5)~~2.464 # unit.

Area of the circle is #A_c= pi*r^2 = pi* (2.464)^2 ~~19.07# sq.unit

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