Learn how to show that a line is tangent to a circle by applying the quadratic formula

The video tutorial explains how to determine if a line is tangent to a circle. It begins by defining a tangent line as one that touches the circle at exactly one point and forms a right angle with the radius. The instructor then demonstrates how to use the Pythagorean theorem to verify if a line is tangent by checking if the theorem holds true, indicating a right angle. The example provided involves calculating squares of given lengths and confirming the equality. The tutorial concludes by applying this method to solve related questions.

What is a key characteristic of a tangent line to a circle?

• It forms an acute angle with the radius.

• It is perpendicular to the radius at the point of contact.

• It is parallel to the radius at the point of contact.

• It passes through two points on the circle.

Which theorem is used to verify if a line is tangent to a circle?

• The Law of Sines

• The Pythagorean Theorem

• The Law of Cosines

• The Triangle Inequality Theorem

In the given example, what is the result of 9 squared plus 40 squared?

• 1,521

• 1,681

• 1,600

• 1,721

What conclusion can be drawn if the Pythagorean theorem holds true for a line and a circle?

• The line is parallel to the circle.

• The line is not tangent to the circle.

• The line is tangent to the circle.

• The line intersects the circle at two points.

What should you do to verify if a line is tangent to a circle in the given questions?

• Verify if the Pythagorean theorem holds.

• Count the number of points the line intersects the circle.

• Check if the line is parallel to the circle.

• Measure the angle between the line and the circle.