Answer:
x = 2
Step-by-step explanation:
AE is equal to the sum of AB and BE because of segment addition postulate, we can substitute to get AE = 11 + x + 1 = x + 12
DE is equal to the sum of DC and CE because of segment addition postulate, we can substitute to get DE = 1 + x + 4 = x + 5
To solve the problem, we can use power of a point, more specifically exterior secants products scenario. In this case, we can get the equation:
AE * BE = DE * CE
Now, we can substitute and solve:
(x + 12)(x + 1) = (x + 5)(x + 4)
x^2 + 13x + 12 = x^2 + 9x + 20
13x + 12 = 9x + 20
4x + 12 = 20
4x = 8
x = 2
