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In the given figure, PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant as shown in the figure. What is the area (in cm2) of the circle?

In the given figure, PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant as shown in the figure. What is the area (in cm2) of the circle? Correct Answer 462 - 308√2

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Given the radius of the bigger circle is 7 cm and suppose radius of the smaller circle is r cm,

⇒ From the figure we can say distance, QO = (7 - r)

Now applying the Pythagoras formula in ΔQOT,

⇒ (7 - r)2 = r2 + r2

⇒ 7 - r = r√2

⇒ r = 7/(√2 + 1) = 7(√2 - 1)

Area of the circle = πr2

⇒ 22/7 × 7 × 7 × (√2 - 1)2

⇒ 22 × 7 × (3 - 2√2)

⇒ 462 - 308√2

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