Problem:
A tangent to a circle at the point P from A is 24 cm long. If O is the centre of the circle and OA = 26 cm, find the diameter of the circle.

Solution:

Step 1: Understanding the Problem
We are given a circle with center O and a tangent AP. The length of OA is 26 cm, and we need to find the diameter of the circle.

Step 2: Defining the Problem
Let's denote the diameter of the circle as 2r. We need to find the value of r.

Step 3: Visualizing the Problem
To better understand the problem, let's draw a diagram.

```
O
/ \
/ \
/ \
A P
```

Step 4: Identifying Key Information
We are given:
- Length of OA = 26 cm
- Length of AP = 24 cm

Step 5: Applying Key Concepts
- OA is the radius of the circle, and AP is a tangent to the circle at point P.
- In a right triangle, the length of the hypotenuse is always greater than the length of either of the other two sides.
- Therefore, in triangle OAP, OA = radius < ap="tangent" />

Step 6: Solving the Problem
Triangle OAP is a right triangle, where OA is the hypotenuse. We can apply the Pythagorean theorem to find the length of OP (the other leg of the triangle).

Using the Pythagorean theorem:
OA² = AP² + OP²
26² = 24² + OP²
676 = 576 + OP²
OP² = 676 - 576
OP² = 100

Taking the square root of both sides:
OP = √100
OP = 10 cm

Since OP is the radius of the circle, the diameter of the circle is 2 * OP.
Diameter = 2 * 10 cm = 20 cm

Therefore, the diameter of the circle is 20 cm.

Summary:
Given a tangent AP of length 24 cm to a circle with center O and OA = 26 cm, we can find the diameter of the circle as 20 cm. Using the Pythagorean theorem, we determined that the length of OP is 10 cm. Since OP is the radius of the circle, the diameter is twice the radius, giving a diameter of 20 cm.