8-6 Segment Lengths (Power Theorems)

Front

What is the Power Theorem in geometry?

Back

The Power Theorem states that if a point is outside a circle, the power of the point is equal to the product of the lengths of the segments from the point to the circle.

Front

How do you find the length of a segment using the Power Theorem?

Back

To find the length of a segment using the Power Theorem, you can use the formula: (length of tangent segment)² = (length of secant segment) × (length of whole secant segment).

Front

If a tangent segment measures 4 units, what is the power of the point?

Back

The power of the point is 4² = 16 square units.

Front

What is a secant segment?

Back

A secant segment is a line segment that intersects a circle at two points.

Front

If a secant segment measures 10 units and the external part measures 6 units, what is the length of the internal part?

Back

Using the Power Theorem: (external part) × (whole secant) = (internal part) × (whole secant). Thus, 6 × 10 = internal part × 10, so the internal part is 4 units.

Front

What is the relationship between tangent segments and secant segments?

Back

The square of the length of a tangent segment is equal to the product of the lengths of the secant segment and its external part.

Front

If a secant segment is divided into two parts of lengths 3 and 5, what is the length of the whole secant segment?

Back

The length of the whole secant segment is 3 + 5 = 8 units.

Front

What is the formula for the Power Theorem?

Back

The formula is: (length of tangent)² = (length of secant) × (length of external part of secant).

Front

How do you solve for 'x' in the equation 8(x+8)=12²?

Back

First, calculate 12² = 144. Then, divide both sides by 8: x + 8 = 144/8 = 18. Finally, subtract 8 from both sides: x = 10.

Front

If a tangent segment is 5 units long, what is the power of the point?

Back

The power of the point is 5² = 25 square units.