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(1) Points $A$, $B$, and $C$ are on sides $\overline{WX}$, $\overline{YZ}$, and $\overline{XY}$ of rectangle $WXYZ$ as shown below such that $XA = 4$, $YB = 18$, $\angle ACB= 90^\circ$, and $YC = 2XC$. Find $AB$.

 

Picture: https://latex.artofproblemsolving.com/0/6/1/061230f0b1b17bcd40886b56dbcbbc0368db13b5.png

 

(2) In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?

 May 5, 2020
 #1
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Please fix LaTeX.

 May 5, 2020
 #2
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Agreed. Raw latex code is tricky to read and also, I'm pretty sure these are questions fromAoPS Intro to Geometry, since they are familiar, so please on't cheat, and if you are, take the time to properly display your latex. Melody would agree.

hugomimihu  May 5, 2020
 #3
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1. AB = 15*sqrt(11).

 

2. The answer is 18*sqrt(2).

 May 9, 2020

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