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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