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[strawberry]

can someone do this question:

A circular metal plate is cut into two segments along a chord equal in length to the radius. What is the ratio of the areas of the two segments?

 

[Affinity]

the chord subtends an angle of Pi/3 (60 degrees) at the center.
This could be seen by joining the 2 extremities of the chord to the center and a equilateral triangle is formed

the area of the major segment = area of major sector + triangle
= (1/2)(5Pi/3) * r^2 + (1/2)(sin Pi/3)*r^2
= [5Pi/6 + sqrt(3)/4]*r^2

The area of the minor segment = area of minor sector - triangle
= (1/2)(Pi/3) * r^2 - (1/2)(sin Pi/3)*r^2
= [Pi/6 - sqrt(3)/4]*r^2

their ratio would be

[5Pi/6 + sqrt(3)/4]*r^2 / [Pi/6 - sqrt(3)/4]*r^2

=[5Pi/6 + sqrt(3)/4] / [Pi/6 - sqrt(3)/4]

= [10Pi/3 + sqrt(3)] / [2Pi/3 - sqrt(3)]

well you might want to simplify further