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Math Challenge II-A Geometry

 
 
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Math Challenge II-A Geometry
by Benjamin Yu - Sunday, June 23, 2024, 9:34 PM
 

Can I have some help with question 5.21 please?

Thank you.

 
Picture of John Lensmire
Re: Math Challenge II-A Geometry
by John Lensmire - Monday, June 24, 2024, 11:28 AM
 

Start by reviewing Example 5.1 (proving the perpendicular bisectors are concurrent).

The general trick is the following:

  • Start with two angle bisectors, say of $A$ and $B$ we know these two lines intersect at one point (call it $G$).
  • Connect $C$ to $G$, our goal now is to prove that $\overline{CG}$ is actually an angle bisector as well.

Hint: Try to use congruent triangles to help.