PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant. What is the area of the circle(in cm²)? |
154 (3 - 2\(\sqrt{2}\)) 308 (3 - 2\(\sqrt{2}\)) 308 (3 + 2\(\sqrt{2}\)) 154 (3 + 2\(\sqrt{2}\)) |
154 (3 - 2\(\sqrt{2}\)) |
QR = 7 cm., QT = \(x\) cm, OT = OU = r cm, QU = QO + OU = 2r + \(x\) = 7cm. ............(i) OQ = \(\sqrt {QS^2 + OS^2}\) = \(\sqrt {r^2 + r^2}\) ⇒ \(x\) + r = \(\sqrt {2}\)r ⇒ \(x\) = (\(\sqrt {2}\) - 1) r From (i) 2r + (\(\sqrt {2}\) - 1) r = 7 r (\(\sqrt {2}\) + 1) = 7 r = \(\frac{7}{\sqrt {2} + 1}\) = 7 (\(\sqrt {2}\) - 1) ⇒ Area of Circle = \(\pi \) r2 = \(\frac{22}{7}\) × 7 × 7 (\(\sqrt {2}\) - 1)2 = 154 (2 + 1 - 2\(\sqrt {2}\)) =154 (3 - 2\(\sqrt {2}\)) |