The diameter of the circle AC and BD intersect at an angle of 90. The length of the arc BC is 4π cm

| April 27, 2021 | education

The diameter of the circle AC and BD intersect at an angle of 90. The length of the arc BC is 4π cm. Find: the radius of the circle; lengths of chords with endpoints at points A, B, C, D.

Since the diameters of AC and BD intersect at an angle of 90, the diagonals divide the circle into four identical arcs, the lengths of which are 4 * n. Then the circumference will be equal to:

C = 4 * 4 * n = 16 * n.

Using the formula for the circumference of a circle, we determine the radius of the circle.

C = 2 * n * R = 16 * n.

R = 16 * p / 2 * p = 8 cm.

Triangles AOB = BCO = COD = AOD so kA are formed by the intersection of the diagonals AC and BD of the square ABCD.

The lengths of the chords AB = BC = CD = AD and are equal to the length of the hypotenuse of right-angled triangles.

AB ^ 2 = AO ^ 2 + BO ^ 2 = 64 + 64 = 128.

AB = BC = CD = AD = 8 * √2 cm.

Answer: The radius of the circle is 8 cm, the lengths of the chords are 8 * √2 cm.



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