Question : Two circles having equal radii intersect each other such that each passes through the centre of the other. The sum of the diameter of these two circles is 84 cm. What is the length of the common chord?

Option 1: $21 \sqrt{3}\ \text{cm}$

Option 2: $14 \sqrt{3}\ \text{cm}$

Option 3: $28 \sqrt{3}\ \text{cm}$

Option 4: $24 \sqrt{3} \ \text{cm}$

Question : Two equal circles of radius 6 cm intersect each other such that each passes through the centre of the other. The length (in cm) of the common chord is:

Option 1: $5 \sqrt{3}$

Option 2: $6 \sqrt{3}$

Option 3: $4 \sqrt{3}$

Option 4: $3 \sqrt{3}$

Question : Two circles having radii of $r$ units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is:

Option 1: $\sqrt{2}r\ \text{units}$

Option 2: $\sqrt{3}r\ \text{units}$

Option 3: $\sqrt{5}r\ \text{units}$

Option 4: $r\ \text{units}$

Question : Two circles touch each other internally. Their radii are 3 cm and 4 cm. What is the length of the biggest chord of the circle with radii of 4 cm which is outside the inner circle?

Option 1: $5 \sqrt{3} \mathrm{~cm}$

Option 2: $6 \sqrt{3} \mathrm{~cm}$

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

Option 4: $2 \sqrt{3} \mathrm{~cm}$

Question : The length of the chord of a circle is 8 cm and the perpendicular distance between the centre and the chord is 3 cm, then the diameter of the circle is equal to:

Option 1: 5 cm

Option 2: 10 cm

Option 3: 3 cm

Option 4: 7 cm