Line AB touches a circle with center at point O and radius equal to 9. Find AB if AO = 41 cm.
| May 30, 2021 | education
From the point O, the center of the circle, we construct the radius OB to the point of tangency B.
The radius drawn to the tangent point is perpendicular to the tangent itself.
Then the angle OBA = 90, and the triangle AOB is rectangular.
In the right-angled triangle AOB, about the Pythagorean theorem, we determine the length of the leg AB.
AB ^ 2 = AO ^ 2 – OB ^ 2 = 1681 – 81 = 160.
AB = 40 cm.
Answer: The length of tangent AB is 40 cm.
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