The following circle (fig.) has two secants from a common point C, namely AC and BC. The circumference of the circle intersects these two secants at E and D respectively. If AE = 6 , BD = 5 and DC = 3, then what is the length of seg DC ?
+128406 I think you want CE , not DC (DC = 3)
We have the secant-secant theorem
CE (CA) = CD (CB)
x ( 6 + x) = 3 ( 3 + 5)
6x + x^2 = 3 * 8
x^2 + 6x = 24 complete the square on x
Take (1/2) of 6 = 3
Square it = 9 and add to both sides
x^2 + 6x + 9 = 24 + 9
(x + 3)^2 = 33 take the positive root
x + 3 =sqrt (33)
x = CE = sqrt (33) - 3 ≈ 2.7446
