Question Number 103062 by ajfour last updated on 12/Jul/20

Commented byajfour last updated on 12/Jul/20

If both coloured regions have  equal areas, find radius of the  semicircle.

Answered by mr W last updated on 12/Jul/20

area of segment:  (R^2 /2)(2θ−sin 2θ)=((πR^2 )/4)  2θ−sin 2θ=(π/2)  ⇒θ=1.1549 (=66.17°)    tan θ=y′=2R sin θ  ⇒R=(1/(2 cos θ))≈1.2376

Commented bymr W last updated on 12/Jul/20

Commented byajfour last updated on 12/Jul/20

Short, succinct and Nice Sir!