AB and BC are chords of a circle with center O, angle ABC = 30 degrees. Find the length of the chord
| August 4, 2021 | education
AB and BC are chords of a circle with center O, angle ABC = 30 degrees. Find the length of the chord AC if the radius of the circle is 10cm.
The inscribed angle ABC rests on the arc AB, then the degree measure of the arc AB is equal to two degree measures of the inscribed angle. Arc AC = 2 * 30 = 60.
Let us construct the radii OA and OC to the edges of the chord AC.
Triangle AOC is isosceles, OA = OC = R = 10 cm.
The central angle AOC rests on the arc AC, then the degree measure of the angle AOC is equal to the degree measure of the arc AC, the angle AOC = 60, and then the triangle AOC is equilateral, which means AC = R = 10 cm.
Answer: The length of the AC chord is 10 cm.
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