Understanding Circles and Chords

This video tutorial covers the fundamental concepts of circles and chords, including definitions of radius, diameter, and chord. It explains the properties of chords, such as perpendicular bisectors and congruent chords, and provides several problem-solving examples. The video also includes word problems to apply these concepts in practical scenarios, using the Pythagorean theorem to find distances and solve for unknowns.

What is the term for the distance from the center of a circle to any point on the circle?

• Circumference

• Radius

• Diameter

• Chord

If a line segment passes through the center of a circle and connects two points on the circle, what is it called?

• Diameter

• Chord

• Tangent

• Radius

What happens when a line from the center of a circle is perpendicular to a chord?

• The chord is bisected

• The chord is doubled

• The circle is divided

• The radius is halved

When are two chords in a circle considered congruent?

• When they are perpendicular

• When they are equidistant from the center

• When they are equal in length

• When they are parallel

If CF is congruent to CG, and AB is 12, what is DE?

• 10

• 12

• 14

• 16

In a circle, if CG is perpendicular to DE, what can be said about DG and GE?

• DG is longer

• They are congruent

• They are parallel

• GE is longer

Given AB = DE and CF = 5x + 3, CG = 7x - 5, what is the value of x?

• 5

• 4

• 3

• 2

If a chord is 6 cm away from the center and 16 cm long, what is the radius of the circle?

• 14 cm

• 12 cm

• 10 cm

• 8 cm

What is the distance from the center to a chord that is 24 cm long if the diameter is 26 cm?

• 5 cm

• 8 cm

• 6 cm

• 7 cm

A 6 by 8 rectangle is inscribed in a circle. What is the radius of the circle?

• 6

• 5

• 7

• 4