To understand how tangents and circles work together, you can follow these simple steps:

1. What is a Tangent?
   A tangent is a line that just touches a circle at one single point. Imagine it like a light brush against the edge of the circle.

2. How does it relate to the Radius?
   The radius is a line from the center of the circle to the edge. When you draw a radius to the point where the tangent touches the circle, it makes a right angle with the tangent line. This means they meet at a 90-degree angle.

3. Proving the Concept:

   • Imagine you have a circle called $O$, and there is a line $L$ that is a tangent at point $A$.
   • Draw the radius $OA$ from the center to point $A$.
   • According to a rule called the Pythagorean theorem, if the line $L$ touches the circle at just point $A$, then the radius $OA$ is at a right angle to the line $L$.

4. An Example:
   Picture point $A$ being located at (4, 3) on a circle that is defined by the equation $x^2 + y^2 = 25$. Here, the radius $OA$ measures 5 units long, and it meets the tangent line at a right angle at that point.

By using these ideas, you can better understand how tangents and circles interact!