Question : $\angle A$ of $\triangle ABC$ is a right angle. $AD$ is perpendicular on $BC$. If $BC= 14$ cm and $BD= 5$ cm, then measure of $AD$ is:

Option 1: $2\sqrt5$ cm

Option 2: $\sqrt5$ cm

Option 3: $3\sqrt5$ cm

Option 4: $3.5\sqrt5$ cm

Question : In $\triangle $ABC, AD$\perp$ BC and AD² = BD × DC. The measure of $\angle$ BAC is:

Option 1: 60°

Option 2: 75°

Option 3: 90°

Option 4: 45°

Question : In a triangle the length of the opposite side of the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?

Option 1: $8\sqrt{2}$ cm

Option 2: $4\sqrt{2}$ cm

Option 3: $8\sqrt{3}$ cm

Option 4: $4\sqrt{3}$ cm

Question : $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$. If $\mathrm{AC}=12 \mathrm{~cm}$, then the length of $\mathrm{BC}$ (in $\mathrm{cm}$) is equal to:

Option 1: $6 \sqrt{2}$

Option 2: $8$

Option 3: $6$

Option 4: $8 \sqrt{2}$

Question : In triangle ABC, $\angle$ABC = 15°. D is a point on BC such that AD = BD. What is the measure of $\angle$ADC (in degrees)?

Option 1: 15

Option 2: 30

Option 3: 45

Option 4: 60