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 :
In the figure, AB = AD = 9 cm, AC = AE = 13 cm, and BC = 15 cm. Find ED.

Option 1: 18 cm

Option 2: 16 cm

Option 3: 14 cm

Option 4: 15 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, PQR is a triangle, and quadrilateral ABCD is inscribed in it. QD = 2 cm, QC = 5 cm, CR = 3 cm, BR = 4 cm, PB = 6 cm, PA = 5 cm and AD = 3 cm. What is the area (in cm²) of the quadrilateral ABCD?

Option 1: $\frac{(23\sqrt{21})}{4}$

Option 2: $\frac{(15\sqrt{21})}{4}$

Option 3: $\frac{(17\sqrt{21})}{5}$

Option 4: $\frac{(23\sqrt{21})}{5}$

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