Understanding Circles

This video tutorial introduces the concept of circles, defining them as a set of points equidistant from a center. It covers key features such as radius, chord, and diameter, and explains secant and tangent lines. The tutorial also explores co-planar circles, including congruent and concentric circles, and discusses how circles can intersect or be tangent to each other. The video concludes with an explanation of common tangent lines between non-intersecting circles.

What is the defining characteristic of a circle?

• It is a set of points equidistant from a center point.

• It is a set of points that form a square.

• It is a set of points that form a straight line.

• It is a set of points that form a triangle.

Which of the following is true about a chord in a circle?

• It is a line segment with endpoints on the circle.

• It is a line that passes through the center of the circle.

• It is a line that touches the circle at one point.

• It is a line that does not intersect the circle.

How is a diameter related to a chord?

• A diameter is a chord that passes through the center.

• A diameter is a chord that does not pass through the center.

• A diameter is a chord that is longer than any other chord.

• A diameter is a chord that is shorter than any other chord.

What distinguishes a tangent line from a secant line?

• A tangent line passes through the center of the circle.

• A tangent line does not intersect the circle.

• A tangent line intersects the circle at two points.

• A tangent line intersects the circle at one point.

What is the point of tangency?

• The point where a chord intersects the circle.

• The point where a tangent line touches the circle.

• The point where a secant line intersects the circle.

• The point where a diameter intersects the circle.

What defines congruent circles?

• Circles that do not intersect each other.

• Circles that are tangent to each other.

• Circles with the same radius but different centers.

• Circles with different radii and the same center.

What are concentric circles?

• Circles that are tangent to each other.

• Circles that intersect at two points.

• Circles that have the same radius but different centers.

• Circles that share the same center but have different radii.

How can two circles be tangent to each other?

• They can only be externally tangent.

• They can only be internally tangent.

• They can be externally or internally tangent.

• They cannot be tangent to each other.

What is a common external tangent line?

• A line that crosses between two circles.

• A line that does not cross between two circles.

• A line that passes through the center of one circle.

• A line that touches only one circle.

What is a common internal tangent line?

• A line that passes through the center of one circle.

• A line that touches only one circle.

• A line that does not cross between two circles.

• A line that crosses between two circles.