Question : In a $\small\triangle P M N$, S is a point on PM that divides PM in the ratio of 5 : 7. The line segment ST is parallel to MN. If MN = 24 cm, then what is the length (in cm) of segment ST?

Option 1: 16

Option 2: 17

Option 3: 14

Option 4: 10

Question : DE is tangent to the circumcircle of $\triangle$ABC at the vertex A such that $DE \parallel BC$. If AB = 17 cm, then the length of AC is equal to:

Option 1: 16 cm

Option 2: 16.8 cm

Option 3: 17.3 cm

Option 4: 17 cm

Question : In an equilateral triangle, the circumradius is 14 cm. What is the length of the median in this triangle?

Option 1: $14 \sqrt{3} \mathrm{~cm}$

Option 2: $21 \mathrm{~cm}$

Option 3: $18 \sqrt{3} \mathrm{~cm}$

Option 4: $7 \sqrt{3} \mathrm{~cm}$

Question : The lengths of the two sides of a triangle are 14 cm and 9 cm. Which of the options below can be the length of the third side?

Option 1: 17 cm

Option 2: 23 cm

Option 3: 24 cm

Option 4: 5 cm

Question : $\triangle$ABC is similar to $\triangle$PQR. If the ratio of the perimeter of $\triangle$ABC and the perimeter of $\triangle$PQR is 24 : 16 and PQ = 4.8 cm, then the length (in cm) of AB is:

Option 1: 8.6

Option 2: 7.2

Option 3: 4.6

Option 4: 2.8

Question : In $\triangle$ABC, the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 16 cm and the length of AQ is 4 cm, then the length (in cm) of CQ is:

Option 1: $(2 \sqrt{21}+2)$

Option 2: $(2 \sqrt{18}-2)$

Option 3: $(2 \sqrt{17}-2)$

Option 4: $(2 \sqrt{19}+2)$