A tangent is drawn from point A to a circle with center O. D is the touch point.
| May 1, 2021 | education
A tangent is drawn from point A to a circle with center O. D is the touch point. Find the radius of the circle if OA = 26 AD = 13√3.
Construct the radius of the OD of the circle, to the point of tangency D.
The radius drawn to the point of tangency is perpendicular to the tangent itself, then the angle ODA = 90, and the triangle AOD is rectangular.
By the Pythagorean theorem, we determine the length of the leg OD.
ОD ^ 2 = ОА ^ 2 – АD ^ 2 = 676 – 507 = 169.
OD = R = 13 cm.
Answer: The radius of the circle is 13 cm.
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