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- #1

- Mar 10, 2012

- 835

- Thread starter caffeinemachine
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- Thread starter
- #1

- Mar 10, 2012

- 835

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- Feb 7, 2012

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Hint: What this does is to construct the line connecting $P$ to the harmonic conjugate of $M$ on the line $AB$ (which happens to be the point at infinity).

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- #3

- Mar 10, 2012

- 835

Thank You. I can conclude now using Ceva's theorem.Draw a random line through $M$, meeting $AP$ at $X$, and $BP$ at $Y$. Let $Z$ be the point of intersection of $BX$ and $AY$. I'll leave you to figure out why $PZ$ is parallel to $AB$.

Hint: What this does is to construct the line connecting $P$ to the harmonic conjugate of $M$ on the line $AB$ (which happens to be the point at infinity).