Tangent Lines and Circles Concepts

This lesson covers tangent lines on a circle, explaining that a tangent line intersects a circle at exactly one point, known as the point of tangency. It discusses the property that a line is tangent to a circle if and only if it is perpendicular to a radius drawn at the point of tangency. The lesson includes two examples where the Pythagorean theorem is used to determine if a line is tangent to a circle by checking for a right angle. The first example confirms tangency, while the second example shows a line is not tangent. The lesson concludes with a summary of these concepts.

What is a tangent line in relation to a circle?

• A line that intersects a circle at two points

• A line that intersects a circle at exactly one point

• A line that does not touch the circle

• A line that is parallel to the circle

What is the point where a tangent line touches a circle called?

• Point of origin

• Point of tangency

• Point of contact

• Point of intersection

A line is tangent to a circle if it is ______ to the radius at the point of tangency.

• Parallel

• Equal

• Perpendicular

• Adjacent

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

• Euclid's theorem

• Thales' theorem

• Fermat's theorem

• Pythagorean theorem

In the first example, what are the side lengths used to apply the Pythagorean theorem?

• 7, 24, 25

• 5, 12, 13

• 9, 40, 41

• 8, 15, 17

In the second example, what is the total length of the side that includes the radius and the outer segment?

• 14

• 16

• 11

• 5

What conclusion is drawn if the Pythagorean theorem does not hold for the given triangle in the second example?

• The line is parallel

• The line is not tangent

• The line is a secant

• The line is tangent