Secant Theorems and Length Calculations

The video tutorial introduces the secant-secant product theorem, explaining its application in geometry. The theorem states that the product of the whole secant segment and its external part is equal for two secants intersecting outside a circle. The tutorial demonstrates this through three problems, each increasing in complexity. The first problem involves basic application, the second introduces more complex numbers, and the third incorporates variables, showcasing the theorem's versatility in solving geometric problems.

What is a secant in relation to a circle?

• A line that touches the circle at one point

• A line that passes through the circle at two points

• A line that is tangent to the circle

• A line that is parallel to the circle

How does the secant secant product theorem relate to chords?

• It is unrelated to chords

• It is similar to the chord chord product theorem

• It only applies to tangent lines

• It is the opposite of the chord chord product theorem

According to the secant secant product theorem, what is multiplied together?

• The whole secant and the diameter

• The whole secant and the internal piece

• The whole secant and the external piece

• The internal piece and the external piece

In the first example, what is the value of x when 14x = 112?

• 6

• 7

• 8

• 9

How do you find the smaller piece of a secant if the whole length and external piece are known?

• Subtract the external piece from the whole length

• Add the whole length and external piece

• Divide the whole length by the external piece

• Multiply the whole length by the external piece

In the second example, what is the whole length of JG?

• 20

• 39

• 16

• 14

What is the value of x when 20x = 351?

• 19.55

• 15.55

• 17.55

• 18.55

In the third example, what is the length of SE if the internal pieces are 8 and 10?

• 22

• 20

• 18

• 16

What is the simplified expression for the whole length of the secant in the third example?

• 2x - 7

• 2x - 10

• 2x - 9

• 2x - 8

What is the value of x when 18x - 72 = 216?

• 12

• 11

• 10

• 13