The degree measure of the inscribed angle is 30 degrees and the length of the chord
| September 25, 2021 | education
The degree measure of the inscribed angle is 30 degrees and the length of the chord on which it rests is -6 cm find the length of the radius of the circle.
Let’s construct the radii OB and OS to the ends of the BC chord.
According to the condition, the value of the inscribed angle of the BAC, resting on the arc of the BC is equal to 30, then the value of the central angle of the BOC, resting on the same arc of the BC, is equal to two values of the inscribed angle.
BOC angle = 2 * 30 = 60.
In the triangle BОС, ОВ = ОС = R, then the triangle BОС is isosceles, and since one of its angles is 60, the triangle BОС is equilateral, which means ОВ = R = ВС = 6 cm.
Answer: The radius of the circle is 6 cm.
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