In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?

Correct option is A

​$$\textbf{Given :} \\\ \, \\AB = AC = 12,\ BC = 5 \\\ \, \\D \text{ lies on } AC \text{ such that } DB = BC \\\ \, \\\textbf{Formula Used :} \\\ \, \\\frac{\text{Corresponding side}_1}{\text{Corresponding side}_2}=\frac{\text{Corresponding side}_2}{\text{Corresponding side}_3} \\\ \, \\\textbf{Solution :} \\\ \, \\AB = AC \Rightarrow \angle ABC = \angle ACB \\\ \, \\DB = BC \Rightarrow \angle BDC = \angle BCD \\\ \, \\\angle ACB = \angle BCD \\\ \, \\\triangle ABC \sim \triangle BCD \\\ \, \\\frac{AC}{BC} = \frac{BC}{CD} \\\ \, \\\frac{12}{5} = \frac{5}{CD} \\\ \, \\12 \cdot CD = 25 \\\ \, \\CD = \frac{25}{12} \\\ \, \\\textbf{Final Answer :} \\\ \, \\\frac{25}{12}$$​​