Circles are fun.. :D
Geometry
Level
3
Give your answers in 3 decimal places.. Understood that the answer will be in cm.. :)
The answer is 3.784.
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1 solution
I see that sin (theta/2)=(x)/(r-x) where theta is the angle of the sector, r is the radius of the bigger circle and x is the radius of the largest circle being inscribed in the sector.. When theta=75/2= 37.5, r=10 and solving for x, we have sin 37.5=(x)/(10-x).. sin 37.5=0.608761429.. Evaluating the aforementioned, we get the answer to be 3.784037944 cm..