Question : If two tangents inclined at an angle of 120° are drawn to a circle of radius 6 cm, then what is the length (in cm) of each tangent?

Option 1: $3 \sqrt{3}$

Option 2: $2 \sqrt{3}$

Option 3: $4 \sqrt{3}$

Option 4: $\sqrt{3}$

Question : Two circles touch each other externally, having a radius of 12 cm and 8 cm, respectively. Find the length of their common tangent AB with point A on the bigger circle and B on the smaller circle.

Option 1: $8 \sqrt{6} \mathrm{~cm}$

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

Option 3: $12 \sqrt{3} \mathrm{~cm}$

Option 4: $12 \sqrt{6} \mathrm{~cm}$

Question : A direct common tangent is drawn to two circles of radius 25 cm and 20 cm. The centres of the two circles are 35 cm apart. What is the length (in cm) of the tangent?

Option 1: $25 \sqrt{2}$

Option 2: $25 \sqrt{3}$

Option 3: $20 \sqrt{3}$

Option 4: $20 \sqrt{2}$

Question : A transverse common tangent is drawn to two circles of radius 8.5 cm and 5.5 cm. The centres of the two circles are 18 cm apart. What is the length (in cm) of the tangent?

Option 1: $10 \sqrt{3}$

Option 2: $10 \sqrt{2}$

Option 3: $8 \sqrt{2}$

Option 4: $8 \sqrt{3}$

Question : In a triangle the length of the opposite side of the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?

Option 1: $8\sqrt{2}$ cm

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

Option 3: $8\sqrt{3}$ cm

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

Question : The radius of a circle is 10 cm. What will be the angle made by a chord of length 20 cm on the circumference of this circle?

Option 1: 90°

Option 2: 120°

Option 3: 180°

Option 4: 135°