Question : In $\triangle$ ABC, $\angle$ BCA = $90^{\circ}$, AC = 24 cm and BC = 10 cm. What is the radius (in cm) of the circumcircle of $\triangle$ ABC?

Option 1: 12.5

Option 2: 13

Option 3: 25

Option 4: 26

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

Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?

Option 1: DF = 5 cm, $\angle$E = 60°

Option 2: DE = 5 cm, $\angle$F = 60°

Option 3:  DE = 5 cm, $\angle$D = 60°

Option 4: DE = 5 cm, $\angle$E = 60°

Question : In a $\triangle ABC$, the bisectors of $\angle$ABC and $\angle$ACB intersect each other at point O. If the $\angle$BOC is 125°, then the $\angle$BAC is equal to:

Option 1: 75°

Option 2: 78°

Option 3: 70°

Option 4: 82°

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