AB is a diameter of a circle. Tangents AD and BC are drawn so that segments AC and BD intersect at a point E on the circle. If AD = a and BC = b, with a ≠ b, then the diameter AB is:
a.  a – b  
b. 


c.  √ab  
d. 


e. 

△AEB is a right triangle, as are △DAB and △ABC. We know α + β = 90°, and we’ll use this information several times. The α’s and β’s show us that △DAB ∼ △ABC, whence a/x = x/b, so x^{2} = ab, and x = √ab. The answer is (c).