<u>Question 1</u>
If we let
, then
.
Also, as
bisects
, this means
.
Thus, by the intersecting chords theorem,

However, as distance must be positive, we only consider the positive case, meaning FE=9
<u>Question 2</u>
If we let CE=x, then because AB bisects CD, CE=ED=x.
We also know that since FB=17, the radius of the circle is 17. So, this means that the diameter is 34, and as AE=2, thus means EB=32.
By the intersecting chords theorem,

However, as distance must be positive, we only consider the positive case, meaning CE=8
increase = 25* .24 = 6 dollars
new price = old price + increase
new price = 25+6
new price = $31
5:3
5 to 3
5/3
Is that what you are looking for?
For complex number, the magnitude is pretty straight forward:
sqrt(6^2 + 2^2) = sqrt(40)
For any a + bi, the magnitude will be sqrt(a^2 + b^2)