A circle is inscribed in the square. find: the radius of the circle if the diagonal of the square = 12√2 cm.

univerkov | March 5, 2021 | education

The diagonal of the square and its two sides form an isosceles right-angled triangle of AСD, in which BP = СD, and hypotenuse AC = 12 * √2 cm.

Then, by the Pythagorean theorem, AC^2 = AD^2 + ВD^2 = 2 * AD^2.

AD^2 = AC^2 / 2 = (12 * √2) ^2/2 = 288/2 = 144.

BP = 12 cm.

Since the side of the square is equal to the diameter of the inscribed circle, its radius will be equal to:

OH = AD / 2 = 12/2 = 6 cm.

Answer: The radius of the inscribed circle is 6 cm.

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