A square with a side equal to 8cm is inscribed in a circle. Find the length of the arc of the circle

| September 27, 2021 | education

A square with a side equal to 8cm is inscribed in a circle. Find the length of the arc of the circle contracted by the side of the square.

A square with a side is inscribed in a circle;

The side of the square is a = 8 cm;

Let us find the length of the arc of the circle contracted by the side of the square.

1) The length of the arc is found by the formula:

L = pi * R * a / 180 °;

R = d / 2;

d = the diagonal of the square.

2) Find the diagonal of the square according to the Pythagorean theorem, if the legs are equal to the side of the square, that is, 8 cm.

d = √ (8 ^ 2 + 8 ^ 2) = √ (64 + 64) = √ (2 * 64) = 8√2 cm;

3) Find the radius of the circle.

R = d / 2 = 8√2 / 2 cm = 8/2 √2 cm = 4√2 cm;

4) The length of the arc is found by the formula:

L = pi * R * a / 180 °;

Angle A = 90 °, then:

L = pi * 4√2 * 90/180 = pi * 4√2 * 1/2 = pi * 2√2 = 2√2pi.



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