How to determine the value of x using the definition of a tangent line to a circle

The video tutorial explains the concept of tangent lines, which intersect a circle at exactly one point and are perpendicular to the circle's radius at the point of intersection. The teacher demonstrates how to prove a line is tangent by using the Pythagorean theorem to show that the line forms a right triangle with the radius. An example problem is provided, where the teacher calculates and verifies the tangency of a line using given measurements, confirming the line is tangent by proving it forms a right angle with the radius.

What is the definition of a tangent line in relation to a circle?

Explain the relationship between a tangent line and the radius of a circle at the point of intersection.

How can we prove that a line is tangent to a circle?

What role does the Pythagorean theorem play in determining if a line is tangent?

What are the steps to verify if a triangle formed by a radius and a tangent line is a right triangle?