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 : If PT is a tangent at T to a circle whose centre is O and OP = 17 cm and OT = 8 cm, find the length of the tangent segment PT.

Option 1: 13 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 15 cm

Question :

In the figure, PT is a tangent. If TP = 12 cm, PB = $x$ + 7 cm, and PA = $x$ cm, then find the value of $x$.

Option 1: 9

Option 2: 6

Option 3: 7

Option 4: 5

Question : DE is a chord and KDE is a secant of a circle. If KD = 9 cm, DE = 7 cm and KH is a tangent to the circle at point H, find KH.

Option 1: 12 cm

Option 2: 25 cm

Option 3: 16 cm

Option 4: 144 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: $3 \sqrt{2} {~cm}$