In the given figure, PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant as shown in the figure. What is the area (in cm2) of the circle?

Answer: Option D

In ΔABQ
AQ² + AB² = BQ²
R² + R² = (7 - R)²
2R² = 49 + R² - 14R
R² + 14R - 49 = 0
∴ R = $$=\frac{-14\pm \sqrt{196+196}}{2}$$
R = -7 ± 7$$\sqrt{2}$$
∴ R = 7$$\sqrt{2}$$ - 7
∴ Area of circle = πR²
= $$\frac{22}{7}$$ × (7$$\sqrt{2}$$ - 7)(7$$\sqrt{2}$$ - 7)
= 154(2 + 1 - 2$$\sqrt{2}$$ )
= 462 - 308$$\sqrt{2}$$