Tangent Lines and Circle Theorems

This video tutorial covers the concepts of tangents and equations of circles, focusing on sections 10.5 and 10.8. It explains tangent lines, common tangents, and theorems related to tangency, such as Theorem 10.10 and Theorem 10.11. The tutorial also demonstrates the use of the Pythagorean Theorem in solving tangency problems and explores circumscribed polygons. Finally, it guides viewers on writing the equation of a circle in standard form.

What is a tangent line?

• A line that is parallel to a circle

• A line that intersects a circle at exactly one point

• A line that intersects a circle at two points

• A line that is inside a circle

How many common tangents can two circles have if they are externally tangent?

• One

• Two

• Four

• Three

According to Theorem 10.10, when is a line tangent to a circle?

• When it is parallel to the radius

• When it is perpendicular to the radius at the point of tangency

• When it is inside the circle

• When it intersects the circle at two points

In the example where KL is tangent to circle J, what theorem is used to justify the answer?

• Theorem 10.12

• Theorem 10.11

• Theorem 10.10

• Theorem 10.9

What is the value of x if JL is the radius of circle J and KL is tangent to circle J?

• 3

• 5

• 9

• 7

What theorem states that if two segments from the same exterior point are tangent to a circle, then they are congruent?

• Theorem 10.9

• Theorem 10.10

• Theorem 10.11

• Theorem 10.12

If AB and CB are tangent to circle D from point B, what can be said about AB and CB?

• AB is shorter than CB

• AB and CB are perpendicular

• AB is congruent to CB

• AB is longer than CB

What is the perimeter of a triangle circumscribed about a circle if the tangents from each vertex to the points of tangency are 8, 7, and 3 units respectively?

• 40 units

• 24 units

• 30 units

• 36 units

What is the standard form of the equation of a circle with center (h, k) and radius r?

• (x - h)^2 + (y - k)^2 = r

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r

• (x + h)^2 + (y + k)^2 = r^2

What is the equation of a circle with center (0, 4) and radius 3?

• (x + 4)^2 + y^2 = 9

• (x - 4)^2 + y^2 = 9

• x^2 + (y + 4)^2 = 9

• x^2 + (y - 4)^2 = 9