# Segments of tangents AB and BC, drawn from point B to a circle with center O

September 29, 2021 | education

| **Segments of tangents AB and BC, drawn from point B to a circle with center O, form an angle equal to 60 degrees, OB = 28 cm. What is the segment AO?**

From the center of the circle, point O, we construct the radii OA and OB, which, by the property of tangents, are perpendicular to AB and BC, then the triangles AOB and BOC are rectangular.

In triangles AOB and BOC, the hypotenuse of OB is common, leg OA = OC = R, and then triangles AOB and BOC are equal in leg and hypotenuse.

Then the angle OBA = OBC = ABC / 2 = 60/2 = 30.

In a right-angled triangle AOB, the leg OA lies opposite an angle of 300, then its length is equal to half the length of the OB hypotenuse. ОА = ОВ / 2 = 28/2 = 14 cm.

Answer: The length of the segment OA is 14 cm.

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