A chord is drawn in a circle with a length of 75 pi, contracting an arc of 120 degrees.

| April 26, 2021 | education

A chord is drawn in a circle with a length of 75 pi, contracting an arc of 120 degrees. Calculate the length of the chord arc data.

Let’s draw the radii of the circle OA and OB. Since the arc AB contracts the arc at 120, the values of the central angle AOB are also equal to 120.

Knowing the length of the circle, we determine its radius.

L = 2 * n * R.

R = L / 2 * n = 75 * n / 2 * n = 75/2 cm.

The triangle AOB is isosceles, then, by the cosine theorem:

AB ^ 2 = AO ^ 2 + BO ^ 2 – 2 * AO * BO * Cos120 = (5625/4) + (5625/4) – 2 * (75/2) * (75/2) * (-1 / 2) = 2 * 5625/4 + 5625/4 = 3 * 5625/4.

AB = 75 * √3 / 2 cm.

Let us determine the length of the arc AB.

Lab = L * 120/360 = 75 * n * 120/360 = 25 * n cm.

Answer: The length of the chord is 75 * √3 / 2 cm, the length of the arc is 25 * n cm.



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