Question : In $\triangle$ ABC, $\angle$ C = 90$^{\circ}$. M and N are the midpoints of sides AB and AC, respectively. CM and BN intersect each other at D and $\angle$ BDC = 90$^{\circ}$. If BC = 8 cm, then the length of BN is:

Option 1: $6 \sqrt{3} {~cm}$

Option 2: $6 \sqrt{6} {~cm}$

Option 3: $4 \sqrt{6} {~cm}$

Option 4: $8 \sqrt{3} {~cm}$

Question : In $\triangle \mathrm{ABC}$, AB = AC, and D is a point on side AC such that BD = BC. If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC?

Option 1: 2 cm

Option 2: 2.5 cm

Option 3: 3 cm

Option 4: 1.8 cm

Question : In a triangle ABC, $\angle$BAC = 90°. If BC = 25 cm, then what is the length of the median AD?

Option 1: 10 cm

Option 2: 12.5 cm

Option 3: 14.5 cm

Option 4: 24 cm

Question : In $\triangle{ABC}, \angle A=90^{\circ}, {AB}=16\ cm $ and $AC =12 \ cm$. $D$ is the midpoint of $AC$ and $DE \perp CB$ at $E$. What is the area (in ${cm}^2$ ) of $\triangle{CDE}$?

Option 1: 8.64

Option 2: 7.68

Option 3: 5.76

Option 4: 6.25

Question : In $\triangle$ABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm.The length of median AD (in cm) is:

Option 1: 4.5

Option 2: 5

Option 3: 4

Option 4: 3