#1**+1 **

To start: Use the length of a bisector theorem: https://proofwiki.org/wiki/Length_of_Angle_Bisector to find AX.

This is not the formula itself, but part of the process in finding the formula. You will see if you click on the link.

The formula that says: AX=ac/(b+c)...

Plug in the coresponding values: 30(21)/(45+21)...

Can you solve that?

ilortyAug 7, 2020

#2**+1 **

Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.

Euclid's Proposition 36, book 3: https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/propIII36.html

Euclid's Proposition 36, book 3 states that ST*SU=SW*SV

Since we want to find SW to get SV, we can change SW to x.

We already know the other lengths:

ST=3

SU=18

SW=x

SV=x-3

So, 3(18)=x(x-3).

From here, we see that when expanded, this becomes 54=x^2-3x.

Solving the quadratic, we see that SW is 12, therefore SV is 9.

EDIT: Or, you could refer to the link in @above....(the steps and reasoning are slightly different, you can look there if you do not understand what I am talking about...)

:)

ilortyAug 7, 2020