AB and BC are tangent line segments drawn to a circle with a center O and a radius of 10 cm
| May 22, 2021 | education
AB and BC are tangent line segments drawn to a circle with a center O and a radius of 10 cm. Find BO if the angle AOC = 60 degrees.
Since BA and BC are tangent to the circle, the radii OA and OС form right angles with the tangents. Then triangles OAB and OCB are rectangular with right angles A and C.
Cuts BO, according to the property of a tangent drawn from one point, divides the angles ABC and BOC in half, then the angle AOB = COB = AOC / 2 = 60/2 = 30.
In a right-angled triangle AOB, we determine the value of the hypotenuse BO.
CosAОВ = AO / BО.
BО = AO / CosAОВ = 10 / (√3 / 2) = 20 / √3 = 20 * √3 / 3 cm.
Answer: The length of the segment BО is 20 * √3 / 3 cm.
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