If radius of circle is 5 cm and distance from centre to the point of intersection of 2 tangents in 13 cm. Find length of tangent.

The radius drawn to the point of tangency is perpendicular to the tangent line, forming a right triangle. Using the Pythagorean theorem, the square of the tangent length plus the square of the radius equals the square of the distance from the center to the external point. This gives the equation length squared plus 5 squared equals 13 squared, so length squared plus 25 equals 169. Subtracting 25 from 169 leaves 144, and taking the square root gives the length of the tangent as 12 cm.

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