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In Poincares disk model in the unit disk, Let $A=(0,0), B=(1/2,0), C=(3/4,0)$, X=(0,1/2) and let $h=\overrightarrow{AX}$

Use Bolyai-Lobatjevskijs formula to calculate the measure of angle between $\overrightarrow{BA}$ and the limit parallel from $B$ to $h$, and between $\overrightarrow{CA}$ and the limit parallel from $C$ to $h$

To start I calculate the distance $h=\overrightarrow{AX}: h=\overrightarrow{AX}=\lvert\ln R[AX,MN]\rvert=\lvert \ln(XO*BP/XP*BO)\rvert=\lvert \ln(3)\rvert=1.0986$

After this I'm not sure how to proceed. I'm unsure how to find distance for $\overrightarrow{XB}$ and $\overrightarrow{XC}$. To use my formula for distance I would need the ideal points of the h-line. I know they are $(0.9831,-0.1831) $and $(-0.1831,0.9831)$ for $\overrightarrow{XB}$ and $(-0.21257,0.97714)$ and $(0.99946,-0.03288) for $\overrightarrow{XC}$. I found them by using the tool on geogebra.org, but I would need to show how to find them algebraically to solve this problem.

How do I find the ideal endpoints of the lines going through $(1/2,0)$ and $(0,1/2)$, or $(3/4,0)$ and $(0,1/2)$

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  • $\begingroup$ A tip enclose everything which is formula into dollar signs \$\$ like \$h=\overrightarrow(AX)=\lvert\$ instead of h=\$\overrightarrow(AX)\$=\$\lvert\$ $\endgroup$ – kingW3 May 16 '17 at 20:55
  • $\begingroup$ Also it should be \$\overrightarrow{AX}\$ with the curly brackets. $\endgroup$ – kingW3 May 16 '17 at 21:05

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