Given information:
- PQ, PR, and BC are tangents to the circle.
- BC touches the circle at point x.
- PQ = 7 cm.

We need to find the perimeter of triangle PBC.

To solve this problem, we will use the properties of tangents and the fact that tangents from a point to a circle are equal in length.

Let's break the solution into steps:

Step 1: Identify the key points and lines in the figure.
- Point P is on the circumference of the circle.
- Point Q is on the tangent PQ.
- Point R is on the tangent PR.
- Point B is on the tangent BC.
- Point C is the point where BC touches the circle.

Step 2: Use the fact that tangents from a point to a circle are equal in length.
- Since BC is a tangent to the circle, BC = Bx.
- Similarly, BC = Cx.

Step 3: Use the fact that tangents from a point to a circle are equal in length.
- Since PQ is a tangent to the circle, PQ = Qx.
- Similarly, PR = Rx.

Step 4: Use the fact that tangents from a point to a circle are equal in length.
- Since PQ = 7 cm and PQ = Qx, Qx = 7 cm.
- Similarly, Rx = 7 cm.

Step 5: Calculate the length of BC.
- Since BC = Bx and BC = Cx, Bx = Cx.
- Let's assume Bx = Cx = y cm.

Step 6: Calculate the perimeter of triangle PBC.
- The perimeter of a triangle is the sum of the lengths of its sides.
- Perimeter of triangle PBC = PQ + BC + CP.
- Since PQ = 7 cm and BC = CP = y cm, the perimeter of triangle PBC = 7 + y + y = 7 + 2y.

Now, let's analyze the given options:

A. 9 cm: If y = 1 cm, the perimeter of triangle PBC = 7 + 2(1) = 9 cm.
B. 12 cm: If y = 2 cm, the perimeter of triangle PBC = 7 + 2(2) = 11 cm.
C. 14 cm: If y = 3 cm, the perimeter of triangle PBC = 7 + 2(3) = 13 cm.
D. 21 cm: If y = 7 cm, the perimeter of triangle PBC = 7 + 2(7) = 21 cm.

Out of the given options, only option D (21 cm) satisfies the condition.

Therefore, the correct answer is option D. The perimeter of triangle PBC is 21 cm.