Question

.. O is centre of circle, ABCD is a square inscribed in the circle. Find the ratio of the perimeter of ABCD and perimeter of the semicircle ABC​

Answer 1

Solution :-

Let us assume that, the radius of circle with centre O is r cm and side of square is a cm .

so,

→ Diameter of circle = Diagonal of square .

→ 2r = √2a

→ a = (2r/√2)

→ a = √2r

then,

→ Perimeter of ABCD : Perimeter of semicircle ABC

→ 4a : (πr + 2r)

→ 4 * √2r : r(π + 2)

→ 4√2 : (π + 2) (Ans.)

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