Question : Let O be the centre of the circle and P be a point outside the circle. If PAB is a secant of the circle which cuts the circle at A and B and PT is the tangent drawn from P, then find the length of PT, if PA = 3 cm and AB = 9 cm.

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

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

Option 3: 6 cm

Option 4: 8 cm

Question : O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?

Option 1: 26 cm

Option 2: 52 cm

Option 3: 13 cm

Option 4: 15 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 : The length of the common chord of two circles of radii 15 cm and 13 cm, whose centres are 14 cm apart, is:

Option 1: 14 cm

Option 2: 12 cm

Option 3: 15 cm

Option 4: 24 cm

Question : In a circle, a 14 cm long chord is 24 cm from the centre of the circle. Find the length of the radius of the circle.

Option 1: 30 cm

Option 2: 25 cm

Option 3: 50 cm

Option 4: 27 cm