Explanation:

Let's analyze the given problem step by step:

- From the point P, a secant PAB intersects the circle at points A and B.

- We are given:

- Distance from the center of the circle to P is 26 cm.

- PB = 32 cm (external segment).

- PA = 18 cm (internal segment).

- We use the Power of a Point Theorem:

- For a point outside a circle, the square of the distance from the point to the center of the circle equals the product of the entire secant and its external segment.

- Mathematically, this is written as \( OP^2 = PA \times PB \).

- Plugging in the values:

- \( 26^2 = 18 \times 32 \).

- Solving this equation:

- \( 676 = 576 \).

- This equation doesn't hold true, which means there might have been a mistake, or we should use another approach.

- Instead, subtract the product from the square of the distance:

- \( R^2 = OP^2 - PA \times PB \) leads you to the solution:

- \( R = \sqrt{676 - 576} \).

- Calculate \( R \):

- \( R = \sqrt{100} = 10 \).

- Option 3: 10 cm.

Thus, Option 3 is the correct one. .