Line AB touches the circle centered at point O and radius 7 cm at point A. Find OB if OBA = 30 degrees.
| June 19, 2021 | education
From the point O, the center of the circle, we construct the radius OA to the point of tangency A.
The radius drawn to the tangent point is perpendicular to the tangent itself.
Then the angle OAB = 90, and the triangle AOB is rectangular.
In a right-angled triangle AOB, leg OA lies opposite angle 30, then its length is equal to half the length of the hypotenuse OA.
ОА = ОВ / 2.
ОВ = 2 * ОА = 2 * 7 = 14 cm.
Answer: The length of the OB segment is 14 cm.
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