Circle Segment Relationships and Theorems

This video tutorial covers segment relationships in circles, focusing on three main theorems: the intersecting chords theorem, the segments of secant theorem, and the secant and tangent theorem. Each theorem is explained with diagrams and example problems to illustrate how to solve for unknown values using these geometric principles.

What is the main focus of this video tutorial?

• Circumference of circles

• Area of circles

• Segment relationships in circles

• Angle relationships in circles

According to the intersecting chords theorem, what is true about the segments of two intersecting chords?

• The ratio of the segments of one chord equals the ratio of the segments of the other chord.

• The difference of the segments of one chord equals the difference of the segments of the other chord.

• The product of the segments of one chord equals the product of the segments of the other chord.

• The sum of the segments of one chord equals the sum of the segments of the other chord.

In the example problem, what equation is set up to solve for x?

• 10x + 7 = 15x - 2

• 10 * 7x = 15 * (5x - 2)

• 10 + 7x = 15 - 5x

• 10 * 7 = 15 * 5x - 2

What is the result of solving the equation 10 * 7x = 15 * (5x - 2)?

• x = 8

• x = 7

• x = 6

• x = 5

What does the segments of secant theorem involve?

• Two chords

• Two tangent segments

• Two secant segments

• A tangent and a chord

In the segments of secant theorem, what is multiplied together?

• The internal segment and the entire segment

• The external segment and the tangent segment

• The external segment and the entire segment

• The external segment and the internal segment

In the example problem for the segments of secant theorem, what is the length of the entire top segment?

• 10

• 9

• 20

• 11

What is the value of x in the example problem for the segments of secant theorem?

• x = 8

• x = 6

• x = 7

• x = 9

What additional segment is introduced in the segments of secant and tangent theorem?

• A chord

• A tangent segment

• A radius

• An arc

In the segments of secant and tangent theorem, how is the tangent segment used?

• It is squared and multiplied by the external segment

• It is added to the secant segment

• It is subtracted from the secant segment

• It is squared and used alone