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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?

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? Correct Answer 11/14

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Let the radius of circle having centre at ‘O’ be ‘r’

⇒ OA = (8 + r) cm and OE = (8 – r) cm

By Pythagoras theorem,

⇒ (8 + r)2 = (8 – r)2 + 42

⇒ 64 + r2 + 16r = 64 + r2 – 16r + 16

⇒ 32r = 16

⇒ r = 1/2 cm

⇒ Area of the circle = πr2

⇒ Area of the circle = (22/7) × (1/2)2

⇒ Area of the circle = 22/ (7 × 2 × 2)

∴ Area of the circle = 11/14 cm

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