Power Theorems in Geometry

This video tutorial covers three power theorems in geometry: the chord-chord power theorem, the tangent-secant power theorem, and the secant-secant power theorem. Each theorem is explained with examples and problem-solving exercises to demonstrate their application in finding missing segment lengths in circles.

What is the chord-chord power theorem used for?

• Calculating the area of a circle

• Finding the length of a tangent

• Determining the product of intersecting chord segments

• Measuring the circumference of a circle

If AE = 8, ED = 12, CE = 16, and BE = x, what is the value of x using the chord-chord power theorem?

• 8

• 6

• 4

• 10

In a chord-chord problem, if CE = 64, CB = 82, and AD = 72, what is AE?

• 16 or 56

• 32 or 40

• 20 or 52

• 24 or 48

What does the tangent-secant power theorem state?

• The tangent is equal to the external part of the secant

• The tangent is twice the length of the secant

• The tangent is equal to the sum of the secant segments

• The square of the tangent is equal to the product of the external part and the entire secant

If CB = 24 and DC = 8, what is the length of AB using the tangent-secant power theorem?

• 8√5

• 12√2

• 10√6

• 16√3

In a tangent-secant problem, if AB = 12 and BC = 9, what is the length of CD?

• 5

• 7

• 9

• 11

What is the secant-secant power theorem used for?

• Calculating the product of external and entire secant segments

• Finding the area of a triangle

• Measuring the diameter of a circle

• Determining the length of a tangent

If ED = 20, DC = 10, and BC = 15, what is the length of AB using the secant-secant power theorem?

• 10

• 15

• 5

• 20

In a secant-secant problem, if AC = 24, AB = 20, and ED = 4, what is EC?

• 10

• 14

• 12

• 8

If AF = 9, EF = 3, BC = 12, and DC = 18, what is the measure of DF?

• 12

• 15

• 18

• 21