Question 88

A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area of the circle?

Solution

Length of AC = $$14\sqrt{2}$$ cm

Let side of square = $$x$$ cm = Diameter of circle

In $$\triangle$$ ABC, => $$(AB)^2 + (BC)^2 = (AC)^2$$

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

=> $$2x^2 = 392$$

=> $$x^2 = \frac{392}{2} = 196$$

=> $$x = \sqrt{196} = 14$$ cm

Thus radius of circle = $$\frac{14}{2} = 7$$ cm

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

= $$\frac{22}{7} \times (7)^2 = 22 \times 7 = 154 cm^2$$

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