Question

If AB = 2.5, CD = 3, and FE = 5, calculate the values of line segment AE and line segment CE . All lines that appear to be tangent to the circle are tangent to the circle.

Answer 1

A B = A F = 2.5B C = C D = 3F E = D E = 5
A E = A F + F E = 2.5 + 5 = 7.5C E = C D + D E = 3 + 5 = 8.0*****************************************************************

Answer 2

according to the Two Tangents Theorem, two segments tangent to a circle from a common point are congruent.
you are given AB=2.5 so FA =2.5 you can add that to the given FE = 5 to get the measure AE= 7.5
Next you are given CD = 3 you can add that to DE= 5 (because of the theorem this is congruent to the given FE) so CE= 8