From a point distant from the center of the circle at a distance of 5 cm, a tangent to it with
| May 27, 2021 | education
From a point distant from the center of the circle at a distance of 5 cm, a tangent to it with a length of 3 is drawn, find the radius of the circle.
From point O, the center of the circle, construct the radius OB to the point of tangency.
The radius drawn to the point of tangency is perpendicular to the tangent itself, then OB is perpendicular to AB, which means triangle AOB is rectangular.
By the Pythagorean theorem, we determine the length of the leg OB.
OB ^ 2 = OA ^ 2 – AB ^ 2 = 25 – 9 = 16.
ОВ = R = 4 cm.
Answer: The radius of the circle is 4 cm.
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