Question

100 POINTS, NEED HELP ASAP

Answer 1

`\textsf{a)} \quad BC^2=CD \cdot CF`

`\text{b)} \quad BC=12\; \sf inches`

Explanation:

Part (a)

The relationship among the lengths of the segments formed by the secant, CD, and the tangent segment, BC, is that the square of the measure of the tangent segment, BC, is equal to the product of the measures of the secant segment, CD, and its external secant segment, CF.

Therefore, the equation is:

`BC^2=CD \cdot CF`

Part (b)

Yes, it is possible to find the length of BC.

Using the equation above, we can substitute in the given values of CD and CF and solve for BC:

`\begin{aligned}BC^2&=CD \cdot CF\\&=16 \cdot 9\\&=144 \end{aligned}`

Square root both sides of the equation:

`\begin{aligned} √(BC^2)&=√(144)\\BC&=12\end{aligned}`

Therefore, the length of BC is 12 inches.