Solving Equations and Circle Properties

The video tutorial explains the concept of congruent chords in a circle, highlighting that congruent chords are equidistant from the circle's center. It demonstrates how to set up and solve an equation to find the value of X, which is then used to calculate the length of a chord segment, OP. The tutorial emphasizes the importance of verifying the solution by checking the problem's requirements.

What is the significance of point O in the context of the circle?

• It is the endpoint of chord CD.

• It is the midpoint of chord AB.

• It is the center of the circle.

• It is a random point on the circle.

What does it mean when two chords are congruent?

• They are parallel to each other.

• They have the same length.

• They intersect at the center.

• They are perpendicular to each other.

According to the theorem, what is true about two congruent chords in a circle?

• They intersect at the center.

• They are equidistant from the center.

• They are perpendicular to the radius.

• They are always parallel.

What equation is set up to find the value of x?

• 12x + 5 = 4x + 19

• 12x - 5 = 4x - 19

• 12x - 5 = 4x + 19

• 12x + 5 = 4x - 19

What is the first step in solving the equation 12x - 5 = 4x + 19?

• Divide both sides by 8.

• Subtract 4x from both sides.

• Multiply both sides by 2.

• Add 5 to both sides.

After solving the equation, what is the value of x?

• x = 5

• x = 2

• x = 3

• x = 4

What is the final step to find the length of OP?

• Subtract 5 from x.

• Multiply x by 5.

• Plug x into the equation for OP.

• Add 5 to x.

What is the length of OP after substituting the value of x?

• 33

• 29

• 35

• 31