A tangent line AB (B is a tangency point) and a secant line intersecting the circle at points C and K

A tangent line AB (B is a tangency point) and a secant line intersecting the circle at points C and K are drawn through point A so that AC = 4 cm, AK = 16 cm.Find the length AB

To find the length of the tangent line segment AB, use the property of the tangent line, according to which, the square of the tangent line segment is equal to the product of the segments cut off by the circle by the secant: AB² = AC ∙ AK. By the condition of the problem, through the outer point A to the circle, a tangent AB (B is the tangency point) and a secant AK are drawn, intersecting the circle at points C and K so that AC = 4 cm, AK = 16 cm.
AB² = 4 cm ∙ 16 cm; AB² = 64 cm²; AB = 8 cm.
Answer: the length of the tangent line segment AB = 8 cm.