Question : The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is:

Option 1: 5 cm

Option 2: 6 cm

Option 3: 7 cm

Option 4: 8 cm

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 : 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 : 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 : Point O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, point P is taken. From this point, two tangents, PQ and PR, are drawn to the circle. Then, the area of quadrilateral PQOR is:

Option 1: $60\ \text{cm}^2$

Option 2: $32.5\ \text{cm}^2$

Option 3: $65\ \text{cm}^2$

Option 4: $30\ \text{cm}^2$