Question :
In the figure, O is the centre of the circle. Its two chords AB and CD intersect each other at the point P within the circle. If AB = 20 cm, PB = 12 cm, and CP = 8 cm, then find the measure of PD.

Option 1: 12 cm

Option 2: 11 cm

Option 3: 22 cm

Option 4: 14 cm

Question : In the following figure, O is the centre of the circle. Its two chords AB and CD intersect each other at point P inside the circle. If AB =18 cm, PB = 6 cm, and CP = 4 cm, then find the measure of PD.

Option 1: 14 cm

Option 2: 18 cm

Option 3: 16 cm

Option 4: 20 cm

Question : In the given figure, the diameter AB and chord CD of a circle meet at P. PT is tangent to the circle at T. If CD = 8 cm, PD = 10 cm, and PB = 8 cm, find AB.

Option 1: 14.5 cm

Option 2: 22.5 cm

Option 3: 12 cm

Option 4: 8 cm

Question : Two chords of a circle, $\overline{\mathrm{AB}}$ and $\overline{\mathrm{CD}}$, meet outside the circle at the point $\mathrm{P}$. If $\mathrm{m}(\overline{\mathrm{AP}})=200 \mathrm{~mm}, \mathrm{~m}(\overline{\mathrm{AB}})$ $=120 \mathrm{~mm}$, and $\mathrm{m}(\mathrm{CP}) = 160 \mathrm{~mm}$, what is the length of $\mathrm{CD}$?

Option 1: 100 mm

Option 2: 75 mm

Option 3: 60 mm

Option 4: 150 mm

Question : A circle touches all four sides of a quadrilateral ABCD. If AB = 18 cm, BC = 21 cm, and AD = 15 cm, then length CD is:

Option 1: 16 cm

Option 2: 14 cm

Option 3: 12 cm

Option 4: 18 cm