Question : Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.

Option 1: $3\sqrt{2}$ cm

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

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

Option 4: $6\sqrt{2}$ cm

Question : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.

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

Option 2: $8 \sqrt{3} \mathrm{~cm}$

Option 3: $8 \sqrt{2} \mathrm{~cm}$

Option 4: $8 \sqrt{6} \mathrm{~cm}$

Question : There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and the radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O and A, respectively. The length of BC is:

Option 1: $2 \sqrt{118} $ cm

Option 2: $2 \sqrt{119} $ cm

Option 3: $2 \sqrt{113} $ cm

Option 4: $2 \sqrt{117}$ cm

Question : If two circles of radii 18 cm and 8 cm touch externally, then the length of a direct common tangent is:

Option 1: 24 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 12 cm

Question : P and Q are centre of two circles with radii 9 cm and 2 cm respectively, where PQ = 17 cm. R is the centre of another circle of radius $x$ cm, which touches each of the above two circles externally. If $\angle PRQ=90^{\circ}$, then the value of $x$ is:

Option 1: 4 cm

Option 2: 6 cm

Option 3: 7 cm

Option 4: 8 cm