In the given figure, PQRS is a square whose side is 8 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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 11/14
Let the radius of circle = r
OT = 8 - r
∠OTP = 90o
Therefore, PQRS is a quadrant
PO = 8 + r
In △OTP,
(8 + r)2 = 42 + (8 - r)2
⇒ 64 + r2 + 16r = 16 + 64 + r2 - 16r
⇒ 32r = 16
⇒ r = 1/2
Hence,
Area of circle = 22/7 × 1/2 × 1/2 = 22/28 = 11/14 cm2