Question : In $\triangle$ABC, D and E are points on the sides BC and AB, respectively, such that $\angle$ACB = $\angle$ DEB. If AB = 12 cm, BE = 5 cm and BD : CD = 1 : 2, then BC is equal to:

Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm, and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:

Question : In equilateral $\triangle $ABC, D and E are points on the sides AB and AC, respectively, such that AD = CE. BE and CD intersect at F. The measure (in degrees) of $\angle $CFB is:

Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE : BC = 6 : 7. (Area of $\triangle {ADE}$ ) : (Area of trapezium BCED) = ?