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 a tangent line in relation to a circle?

• A line that intersects a circle at two points

• A line that is inside the circle

• A line that is parallel to a radius of the circle

• A line that intersects a circle at exactly one point

Why is the perpendicularity of a tangent line important?

• It allows us to determine if a line is tangent using the Pythagorean theorem

• It is used to find the circumference of the circle

• It helps in calculating the area of the circle

• It is necessary for drawing a circle

Which theorem is used to prove that a line is tangent to a circle?

• Theorem of Congruent Angles

• Pythagorean Theorem

• Theorem of Similar Triangles

• Theorem of Parallel Lines

In the example provided, what is the length of the radius used?

• 9

• 8

• 15

• 17

What does the Pythagorean theorem prove in the context of the example?

• The line is parallel to the radius

• The line is tangent to the circle

• The circle is a perfect circle

• The line is inside the circle