Question : In $\triangle$ABC, the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 16 cm and the length of AQ is 4 cm, then the length (in cm) of CQ is:

Question : In $\Delta ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC,$ respectively in such a way that $AC$ is parallel to $DE$. Then $\Delta ABC$ and $\Delta DBE$ are:

Question : D and E are points on sides AB and AC of $\Delta ABC$. DE is parallel to BC. If AD : DB = 2 : 3. What is the ratio of the area of $\Delta ADE$ and the area of quadrilateral BDEC?

Question : $\Delta ABC$ and $\Delta DEF$ are similar. Also $\angle A=\angle D$ and $\angle B=\angle E$. If $4AB=DE$ and $BC=\operatorname{12 cm}$, then $EF$ is equal to:

Question : The centroid of an equilateral triangle $ABC$ is $G$ and $AB = 10 \:\operatorname{ cm}$. The length of $AG$ is: