In a circle with radius 4 cm the diameters ac and bd are perpendicular to each other. prove that abcd is a square. find the area of abcd.

To prove that ABCD is a square we will use the Pythagoras theorem. and we must know the Property of the square.

In ABCD all the sides are equal and diagonals are perpendicular and equal to each other, therefore, ABCD is a square.

1. In ΔAOB

AO = BO = r, radius of the circle O,

2. In ΔBOC

BO = CO = r, radius of the circle O,

3. In ΔCOD

CO = DO = r, radius of the circle O,

4. In ΔAOD

AO = DO = r, radius of the circle O,

Thus, AB = BC = CD =DA = r√2.

Hence, In ABCD all the sides are equal and diagonals are perpendicular and equal to each other, therefore, ABCD is a square.

Learn more about Property of square:

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step-by-step explanation:

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