Question : A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, then the radius of the circle is:

Option 1: $2 \sqrt{3} {~cm}$

Option 2: $\sqrt{19} {~cm}$

Option 3: $\sqrt{17} {~cm}$

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

Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

Option 1: $5 \sqrt{5}$ cm

Option 2: $5 \sqrt{2}$ cm

Option 3: $5$ cm

Option 4: $5 \sqrt{3}$ cm

Question : In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of the chord PQ is:

Option 1: $2\sqrt{13}\;\mathrm{cm}$

Option 2: $5\sqrt{3}\;\mathrm{cm}$

Option 3: $4\sqrt{6}\;\mathrm{cm}$ 

Option 4: $6\sqrt{5}\;\mathrm{cm}$

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 : A tangent is drawn from a point M to a circle, which meets the circle at T such that MT = 12 cm. A secant MAB intersects the circle at points A and B. If MA = 8 cm, what is the length (in cm) of the chord AB?

Option 1: 16

Option 2: 10

Option 3: 12

Option 4: 9