Question : Two medians NA and OB of $\triangle \mathrm{NOP}$ intersect each other at S at right angles. If NA = 15 cm and OB = 15 cm, then what is the length of OA?

Option 1: $5 \sqrt{5} $ cm

Option 2: $7 \sqrt{5}$ cm

Option 3: $6 \sqrt{5}$ cm

Option 4: $3 \sqrt{5}$ cm

Question : Two medians JX and KY of $\triangle \mathrm{JKL}$ intersect each other at Z at right angles. If KL = 22 cm and KY = 12 cm, then what is the length of JX?

Option 1: $6 \sqrt{19} \mathrm{~cm}$

Option 2: $3 \sqrt{57} \mathrm{~cm}$

Option 3: $2 \sqrt{57} \mathrm{~cm}$

Option 4: $4 \sqrt{19} \mathrm{~cm}$

Question : $\triangle DEF$ is right angled at E. EC is the altitude. CF is 18 cm and FD is 26 cm. What is the length of FE?

Option 1: $2\sqrt{13}$ cm

Option 2: $6\sqrt{13}$ cm

Option 3: $12$ cm

Option 4: $15$ cm

Question : In a triangle DEF, DP is the bisector of $\angle D$, meeting EF at P. If DE = 14 cm, DF = 21 cm and EF = 9 cm, find EP.

Option 1: 3.6 cm

Option 2: 5.4 cm

Option 3: 6.3 cm

Option 4: 2.7 cm

Question : Two circles of radii 15 and 18 cm touch each other externally. What is the length (in cm) of the direct common tangent to the two circles?

Option 1: $18 \sqrt{6}$

Option 2: $12 \sqrt{15}$

Option 3: $30 \sqrt{6}$

Option 4: $6 \sqrt{30}$