D is a point on the side BC of a $\triangle$ABC such that $\angle ADC = \angle BAC$. If CA = 10 cm and BC = 16 cm then the length of CD is:
Answer & explanation
Correct answer: option 3
\(\Delta \)DCA is similar to \(\Delta \)ACB
\(\frac{CD}{AC}\) = \(\frac{AC}{BC}\)
= \(\frac{CD}{AC}\) = \(\frac{10}{16}\)
= CD = \(\frac{10 \;×\; 10}{16}\) = 6.25 cm.