A tangent CK is drawn to a circle with center O, K is a tangent point, find the area of a triangle CОК
| April 11, 2021 | education
A tangent CK is drawn to a circle with center O, K is a tangent point, find the area of a triangle CОК if the angle ОCК = 30 •, and the radius of the circle = 8
Construct the radius OK to the point of tangency K.
The radius OK, drawn to the point of tangency K, is perpendicular to the tangent CK itself, then the angle OCK = 90, and the triangle OCK is rectangular.
In a right-angled triangle OCK tg30 = OK / CK.
CK = OK / tg30 = 8 / (√3 / 3) = 8 * √3 cm.
Determine the area of the triangle OCK.
Sosc = OK * CK / 2 = 8 * 8 * √3 / 2 = 32 * √3 cm2.
Answer: The area of the triangle is 32 * √3 cm2.
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