Question : Circum-centre of $\triangle PQR$ is O. If $\angle QPR=55^{\circ}$ and $\angle QRP=75^{\circ}$, What is the value (in degree) of $\angle OPR$?

Option 1: 45°

Option 2: 40°

Option 3: 65°

Option 4: 70°

Question : PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Measure of $\frac{1}{2} \angle \mathrm{PSQ}$ is:

Option 1: 20°

Option 2: 15°

Option 3: 30°

Option 4: 60°

Question : In $\triangle$PQR, $\angle$ PQR = $90^{\circ}$, PQ = 5 cm and QR = 12 cm. What is the radius (in cm) of the circumcircle of $\triangle$PQR?

Option 1: 6.5

Option 2: 7.5

Option 3: 13

Option 4: 15

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 $\triangle \mathrm{ABC}, \angle \mathrm{A}=68^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle B I C$ is:

Option 1: 124°

Option 2: 68°

Option 3: 148°

Option 4: 54°