To solve this question we will use a theorem called the intersecting secant theorem which states that "if 2 secants of a circle intersect outside the circle then product of their segments are equal".
Thus, applying this theorem in this question we see that:[tex] AC\times BC=EC\times DC [/tex]
Thus, [tex] 10\times 6=12\times DC [/tex]
Thus, [tex] DC\frac{10\times 6}{12}=5 cm [/tex]
Thus, out of the given options, the first option is the correct option.
