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?

Solution (By Examveda Team)

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$$\sqrt 2 $$