In the figure given below, square ABCD is inscribed in a circle.Point E is joined to D and C such that AE = EB. If the area of the triangle is 20 square units find the difference in area of the circle and the square.
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Let the side of the square be A and the radius of the circle be C.
i.e. AB = BC = CD = DA = A and AC = 2*C
We also know that AC is the diagonal of the square ABCD.
i.e. AC = 2*C = √2 * A => C = A/√2
Area of the Triangle DEC = (1/2)*Base*Height = (1/2) * CD * BC = (1/2)*A*A = 20 Square units
i.e. A*A = 40, A = 2√10 .
Radius of the circle = C = A/√2 = 2√10/√2 = 2√5.
Area of the circle = pi*C*C = pi*2√5*2√5 = pi*20 square units.
Area of the square = A*A = A*A = 40 square units.
Difference is areas = pi*20 - 40
