Question 92
Find the area of a square inscribed in a circle whose radius is 7 cm as shown in the figure.
Hint: Four right-angled triangles joined at right angles to form a square.
Given that ABCD is a square.
According to the question.
Area of square ABCD =4× Area of a right angled triangle
∴ Area of square ABCD=4× Area of ΔAOB
=4×(12×AO×BO)
[∵ area of a right angled triangle =12×base×height]
=2×7×7=98 cm2
[∵ AO = BO = radius of circle = 7 cm, given]
Hence, the area of inscribed square is 98 cm2.