Question

Find the value of c using the given chord and secant lengths in the diagram shown to right . c= (Round to the nearest tenth as needed .)

Answer 1

c = 6.4

Step-by-step explanation

The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.

One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:

`9\cdot(9+19)=13\cdot(13+c)`

Solving for c:

`\begin{gathered} 9\cdot28=13^2+13c \\ 252=169+13c \\ 252-169=13c \\ 83=13c \\ c=(83)/(13) \\ c=6.3846\ldots \\ c\approx6.4 \end{gathered}`