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 : 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 of the same radius 6 cm, intersect each other at P and Q. If PQ = 10 cm, then what is the distance between the centres of the two circles?

Option 1: $10\mathrm{~cm}$

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

Option 3: $6\sqrt{11} \mathrm{~cm}$

Option 4: $2\sqrt{11} \mathrm{~cm}$

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 : Two circles of radius 10 cm and 5 cm touch each other externally at point A. PQ is the direct common tangent of those two circles of centres O₁ and O₂, respectively. The length of PQ is equal to:

Option 1: $10\sqrt{2}$ cm

Option 2: $8\sqrt{2}$ cm

Option 3: $9\sqrt{2}$ cm

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