In the given figure, PQRS is a square whose side is 12 cm. PQS and QPR are two quadrants. A circle is placed touching both the quadrants and the square as shown in the figure. What is the area (in cm2) of the circle ?
Answer & explanation
Correct answer: option 3
Let radius of circle = r
∴ OA = 12 - r, OQ = 12 + r
In ΔOAQ
(OQ)2 = (OA)2 + (AQ)2
(12 + r)2 = (12 - r)2 + 62
144 + r2 + 24r = 144 + r2 - 24r + 36
48r = 36
r = \(\frac{36}{48}\)
r = \(\frac{3}{4}\)
and area of circle = \(\pi \)r2
= \(\frac{22}{7}\) × \(\frac{3}{4}\) × \(\frac{3}{4}\) = \(\frac{99}{56}\) cm2