Question : If the length of each side of a rhombus ABCD is 16 cm and $\angle ABC=120^\circ$, what is the length (in cm) of BD?

Option 1: $24$

Option 2: $12$

Option 3: $16$

Option 4: $14\sqrt{3}$

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 ABC which is equilateral. O is the point of intersection of altitude AL, BM, and CN. If OA = 16 cm, what is the semi-perimeter of the triangle ABC?

Option 1: $8 \sqrt 3$ cm

Option 2: $12 \sqrt 3$ cm

Option 3: $16 \sqrt 3$ cm

Option 4: $24\sqrt 3$ cm

Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:

Option 1: $\sqrt{2} \mathrm{~cm}$

Option 2: $4 \mathrm{~cm}$

Option 3: $2 \sqrt{2} \mathrm{~cm}$

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

Question : If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, $\angle$BGC = $120^{\circ}$, BC = 10 cm, then the area of the triangle ABC is:

Option 1: $50\sqrt{3}$ $cm^2$

Option 2: $60$ $cm^2$

Option 3: $25$ $cm^2$

Option 4: $25\sqrt{3}$ $cm^2$

Question : A chord of length 7 cm subtends an angle of $60^{\circ}$ at the centre of a circle. What is the radius (in cm) of the circle?

Option 1: $7\sqrt{2}$ cm

Option 2: $7\sqrt{3}$ cm

Option 3: $7$ cm

Option 4: $14$ cm