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# How can you find the area of a square in a circle?

Let square ABCD be inscribed in a circle with radius r and center O.

## Answer: The area of the square ABCD is 2r^{2}.

Let's solve it step by step.

**Explanation:**

As given in the above figure, square ABCD is inscribed in a circle with radius 'r' and centre 'O'

Let the sides of the square be 'a'. So, area of the square ABCD will be (side)^{2}.

The diameter of the circle is the diagonal of the square.

⇒ BD = 2r or D (diameter)

Using pythagoras theorem for triangle ABD,

⇒ (AB)^{2 }+ (AD)^{2} = (BD)^{2}

⇒ a^{2 }+ a^{2 } = D^{2 }

⇒ 2a^{2 }= D^{2 }

⇒ a = D / √ 2

⇒ a = 2r / √ 2

Area of square is a^{2} = (2r / √ 2)^{2}

⇒ a^{2} = (4r^{2} / 2)

⇒ a^{2} = 2 r^{2}

### Thus, the area of the square ABCD in the circle is 2 r^{2}.

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