Question

In the accompanying diagram of circle o, chords AB and CD

intersect at E. If AE = 3, EB = 4, CE = x, and ED = x +1,
find CE

Answer 1

x = 3

Explanation:

Given :

AE = 3, EB = 4, CE = x, and ED = x +1,

Equating chord AB and CD

AE*EB = CE*ED

3*4 = x*(x+1)

12 = x² + x

x² + x - 12 = 0

x² +4x - 3x - 12 = 0

x(x + 4) - 3(x + 4)

(x + 4) = 0 or (x - 3) = 0

x = - 4 or x = 3

Distance can't be negative :

x = 3