Find the length of an arc of a circle if the radius drawn to its end makes an angle of 35

Find the length of an arc of a circle if the radius drawn to its end makes an angle of 35 degrees with the chord corresponding to this arc, and the radius of the circle is 12 cm.

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

The AOB triangle is isosceles, since ОА = ОВ = R = 12 cm.

By condition, the angle ОАВ = 35, then the angle ОВА = 35.

Central angle AOB = (180 – OAB = OBA) = (180 – 35 – 35) = 110.

Then the degree measure of the arc AB = 110.

The circumference is: C = 2 * π * R = 24 * π.

Let us determine the length of the arc AB.

L = C * AOB / 360 = 24 * π * 110/360 = 231 * π / 36 = 77 * π / 12.

Answer: The length of a circular arc is 77 * π / 12.