The angle between two tangents drawn from point A is 60 degrees R = 8 cm find the distance from A
| July 1, 2021 | education
The angle between two tangents drawn from point A is 60 degrees R = 8 cm find the distance from A to the center of the circle.
From the center of the circle, point O, draw the radii OB and OC to the tangent points AB and AC.
By the property of the tangent, the radii are perpendicular to the tangents, then the triangles ABO and ACO are rectangular.
By the property of tangents drawn from one point, the OA segment is the bisector of the angle between the tangents, then the angle BAO = CAO = BAC / 2 = 60/2 = 30.
The leg ОВ = R = 8 cm and lies against the angle 30, then BО = AO / 2, and therefore AO = 2 * ОВ = 2 * 8 = 16 cm.
Answer: The distance from point A to the center of the circle is 16 cm.
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