Through point A, two tangents AB and AC are drawn to a circle with a center at point O

Through point A, two tangents AB and AC are drawn to a circle with a center at point O and a radius of 8.5 cm.Find the angle between the tangents if OA = 17 cm.

Since by the property of the tangent, the tangent is perpendicular to the radius of the circle drawn to the tangent point. Then the triangles ABO and AСO are rectangular.

By condition, the hypotenuse of the AO triangle is twice as large as the ВO leg. AO / ВO = 17 / 8.5 = 2.

Then the ВO leg lies opposite the angle 30.

Triangles ABO and AСO are equal on three sides, since AO is a common side, BO and CO are the radii of the circle, AB = AC, since the tangents drawn from one point to the circle are equal.

Then the angle ∠ВАО = ∠САО.

∠ВАС = 2 * ВАО = 2 * 30 = 60.

Answer: The angle between tangents is 60.




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