Question : A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm, and AC = 24 cm, and sides AB, BC, and AC touch circle at D, E, and F, respectively. The measure of AD is:

Question : $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $\triangle ABC$ such that $DE$ is parallel to $BC$ and $AD: DB = 4:5$, $CD$ and $BE$ intersect each other at $F$. Find the ratio of the areas of $\triangle DEF$ and $\triangle CBF$.

Question : If $D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD: DB = 2:3$ and the area of $\Delta ADE$ is 4 sq. cm, what is the area (in sq. cm) of quadrilateral $BDEC$?

Question : In $\triangle \text{ABC}, \mathrm{DE} \| \mathrm{BC}$ and $\frac{\text{AD}}{\text{DB}}=\frac{4}{5}$. If $\mathrm{DE}=12 \mathrm{~cm}$, find the length of $\mathrm{BC}$.

Question : Let D and E be two points on the side BC of $\triangle ABC$ such that AD = AE and $\angle BAD = \angle EAC$. If AB=(3x+1) cm, BD = 9 cm, AC=34 cm and EC = (y + 1) cm, then the value of (x + y) is: