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Find \(AX\) in the diagram if \(CX\) bisects \(\angle ACB\)

 Aug 7, 2020
 #1
avatar+1038 
+5

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?

 Aug 7, 2020
edited by ilorty  Aug 7, 2020
edited by ilorty  Aug 7, 2020
 #2
avatar+21955 
+2

The angle bisector theorem states that if C is the angle bisector, then this formula applies:

   AX / XB  =  AC / BC     --->     AX / 30  =  21 / 45     --->     AX  =  30 · 21 / 45  =  14.

 Aug 7, 2020

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