The chord of the circle is equal to the 3 root of 2 and subtracts the arc of 60 degrees.

| February 4, 2021 | education

The chord of the circle is equal to the 3 root of 2 and subtracts the arc of 60 degrees. Find the arc length and area of the corresponding sector

From the center O of the circle, we construct the radii OA and OB to the ends of the chord.

The degree measure of the arc AB, according to the condition, is 60, then the central angle AOB is equal to the degree measure of the arc AB, the angle AOB = 60.

Since in the triangle AOB, AO = OB = R, and the angle AOB = 60, then triangle AOB is isosceles, and OA = OB = R = 3 * √2 cm.

Let us determine the length of the smaller chord AB.

Lav = n * R * 60/180 = n * 3 * √2 * 60/180 = √2 * p.

Let’s define the area of the OAB sector.

Ssec = n * R2 * 60/360 = n * 18 * 60/360 = 3 * n cm2.

Answer: The length of the arc is √2 * n, the area of the sector is 3 * n cm2.



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