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)?
Answer & explanation
Correct answer: option 1
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\(\sqrt {2}\))