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 : In a $\triangle P Q R, \angle P: \angle Q: \angle R=3: 4: 8$. The shortest side and the longest side of the triangle, respectively, are:

Option 1: PQ and PR

Option 2: QR and PR

Option 3: PQ and QR

Option 4: QR and PQ

Question : In $\Delta PQR,$ $\angle P : \angle Q : \angle R = 1: 3 : 5$, what is the value of $\angle R - \angle P$?

Option 1: $30^\circ$

Option 2: $80^\circ$

Option 3: $45^\circ$

Option 4: $60^\circ$

Question : ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with centre O has been inscribed inside $\triangle ABC$. The radius of the circle is:

Option 1: 1 cm

Option 2: 2 cm

Option 3: 3 cm

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