Question : In $\triangle$ABC, AB = $a - b$, AC = $\sqrt{a^2+b^2}$, and BC = $\sqrt{2ab}$, then find angle B.

Question : In triangle ABC, $\angle$ B = 90°, and $\angle$C = 45°. If AC = $2 \sqrt{2}$ cm then the length of BC is:

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 : 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 : G is the centroid of $\triangle$ABC. If AG = BC, then measure of $\angle$BGC is: