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enter image description here Kindly don't mind the pencil marks. Please also include the solution, thank you!

Elmarie K.
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  • Why did you ask about a circle and tag it spherical trig? Is this in 2D or 3D? Please make it clear. In 2D you want to compare a circular sector to a triangle. In 3D you want a spherical cap. -1 – Ross Millikan Oct 16 '16 at 03:10
  • I apologize, I'm unfamiliar to this site. Anyway, it's a 2D figure. – Elmarie K. Oct 16 '16 at 03:13
  • The fact that the radius is $12$ cm says if you draw radii to the points where the chords intersect the circle you get equilateral triangles. Can you compute the area of those? Can you compute the area of the sectors? Where are you stuck? – Ross Millikan Oct 16 '16 at 03:17

1 Answers1

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To find the area of the shaded portion of the circle, we need to find the area of the 2 segments(they are equal) and subtract that area from the area of the circle

1) lets label the points (points of the intersection of the line with the circle) on the left A and B, and the center O. Since the diameter is 12cm, then the radius is 6cm, then triangle ABC is equilateral, then The angle AOB=pi/3

2) Find the area of the sector AOB. A(AOB)=pir^2((pi/3)/2pi)=6pi 3) Find the area of the triangle AOB. A=rrsin(pi/3)1/2 = 9sqrt(3) 4) The area of the segment is 6pi-9sqrt(3) 5) The area of the circle is pir^2 = 36pi 6) and finally, the area of the shaded portion is:

A = 36pi-2*(6pi-9sqrt(3)) = 36pi-12pi+18sqrt(3) = 24pi+18sqrt(3)

Hope this helps

Armen Barseghyan
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