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:

Given that CA= 10, BC = 16 in the $$\triangle ABC $$

from the above triangle,

   $$ \triangle ABC  and \triangle DAC $$

$$\angle ADC = \angle BAC$$ (given that)

  $$\Rightarrow \angle A = \angle D $$ 

$$ \angle B = \angle DAC  $$

then $$\triangle ABC and $$ BDA $$

$$\Rightarrow \frac {AC} {DC} = \frac{BC}{AC} $$

$$\Rightarrow \frac {10}{CD} = \frac{16}{10} $$ (put the value)

$$\Rightarrow CD = \frac{100}{16} $$

$$\Rightarrow CD = 6.25 $$ CM Ans