Given the circle below with secants start overline, R, S, T, end overline

Question

RST
and start overline, V, U, T, end overline
VUT
, find the length of start overline, R, S, end overline
RS
. Round to the nearest tenth if necessary.
R
T
V
5
4
10
S
U

Answer 1

To find the length of RS, we must first find the length of VT using the following formula:

(RT)(TS) = (VT)(TU)

Given:
RT = 5
TS = 4
VT = x
TU = 10

5 * 4 = x * 10
20 = 10x
x = 2

Now we know that VT = 2. Next, we find the length of RS by adding RT and TS:

RS = RT + TS = 5 + 4 = 9

Therefore, the length of RS is 9 units.