MATH tough questions

  1.   If the area of a circle and a semicircle are equal , if those are placed one top of another in such a way the midpoints are at the exact point when viewed from top . What is the value of Semicircle radius if the value of the circle radius is √2

Solution :  Let us keep radius of the circle = r 

    And  let us keep radius of the semicircle = R 

    As given in this question areas  are equal .   

Area of the circle =

                                 

Area of semicircle  =