Question 70

A square is inscribed in a circle. If the side of the square is 14 cm, what is the area (in sq.cm) of the circle?

Solution

Square is inscribed in circle, thus diagonal of square = diameter of circle

Side of square = BC = CD = 14 cm

In $$\triangle$$ BCD

=> $$BD = \sqrt{(BC)^2 + (CD)^2}$$

=> $$BD = \sqrt{(14)^2 + (14)^2} = \sqrt{196 + 196}$$

=> $$BD = \sqrt{392} = 14\sqrt{2}$$

=> Radius of circle $$r = 7\sqrt{2}$$ cm

$$\therefore$$ Area of circle = $$\pi r^2$$

= $$\pi (7\sqrt{2})^2 = 98 \pi cm^2$$

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