AB and BC are segments of tangents drawn from point B to a circle with center O.
| May 14, 2021 | education
AB and BC are segments of tangents drawn from point B to a circle with center O. AO = 5, OB = 10. what is the angle AOC?
From point O, the center of the circle, draw the radii OA and OC to the points of tangency.
By the property of tangents, the radii drawn to the point of tangency are perpendicular to the tangents, then the angles OAB and OCB are straight.
In a right-angled triangle ОАВ, by condition, ОА = 5 cm, ОВ = 10 cm.
Determine the value of the angle AOB. CosАВ = ОА / ОВ = 5/10 = 1/2.
Angle AOB = arcos (1/2) = 60.
Rectangular triangles OAB and OCB are equal in leg and hypotenuse, OA = OC = R = 5 cm, the hypotenuse of OB is common, then the angle AOB = COB = 60, the angle AOC = 2 * AOC = 2 * 60 = 120.
Answer: The AOC angle is 120.
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