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 : The area of triangle with vertices A(0, 8), O(0, 0), and B(5, 0) is:

Option 1: 8 sq. units

Option 2: 13 sq. units

Option 3: 20 sq. units

Option 4: 40 sq. units

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 : 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 : ABCD is a square inscribed in a circle of radius $r$. Then the total area (in square units) of the portions of the circle lying outside the square is:

Option 1: $\pi (r^{2}-4)$

Option 2: $2\pi (r ^{2}-1)$

Option 3: $\pi^{2} r(r-7)$

Option 4: $r^{2}(\pi -2)$