AB and BC are segments of tangents drawn from point B to a circle with center OA = 16cm

| July 25, 2021 | education

AB and BC are segments of tangents drawn from point B to a circle with center OA = 16cm, and the radii drawn to the points of tangency form an angle equal to 120 degrees. What is the segment OB?

The tangent AB and the radius OA of the circle at the point of their intersection form a right angle by the property of the tangent, then the triangle BOA is rectangular with right angle A.

Triangles ABO and CBO are equal on three sides, OB is a common side, OA and OC are the radii of the circle, AB and BC are equal as tangents drawn from one point. Then the angle BOA = BOC = AOC / 2 = 120/2 = 60.

Then the angle ABO = 180 – 90 – 60 = 30.

The leg OA of the right-angled triangle AOB lies opposite the angle 30, then the hypotenuse BO = 2 * OB = 2 * 16 = 32 cm.

Answer: The length of the ВO segment is 32 cm.



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