A tangent AB (B-tangency point) and a secant line are drawn through point A
| June 27, 2021 | education
A tangent AB (B-tangency point) and a secant line are drawn through point A, which intersects the circle at points E and F. Find EF if AB = 9, AF = 15.
The square of the tangent segment from point A to point B is equal to the product of the lengths of the secant segments from point A to points E and F:
AB² = AE * AF.
9² = AE * 15.
AE = 81: 15 = 5.4.
The AF segment is equal to the sum of the EF and AE segments:
EF = AF – AE = 15 – 5.4 = 9.6.
Answer: The EF segment is 9.6.
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