Whoever wrote this... doesn't know what concise means :\

by shiningsunnyday, Apr 11, 2017, 3:46 PM

2004 ISL G2 wrote:
Let $\Gamma$ be a circle and let $d$ be a line such that $\Gamma$ and $d$ have no common points. Further, let $AB$ be a diameter of the circle $\Gamma$; assume that this diameter $AB$ is perpendicular to the line $d$, and the point $B$ is nearer to the line $d$ than the point $A$. Let $C$ be an arbitrary point on the circle $\Gamma$, different from the points $A$ and $B$. Let $D$ be the point of intersection of the lines $AC$ and $d$. One of the two tangents from the point $D$ to the circle $\Gamma$ touches this circle $\Gamma$ at a point $E$; hereby, we assume that the points $B$ and $E$ lie in the same halfplane with respect to the line $AC$. Denote by $F$ the point of intersection of the lines $BE$ and $d$. Let the line $AF$ intersect the circle $\Gamma$ at a point $G$, different from $A$. Prove that the reflection of the point $G$ in the line $AB$ lies on the line $CF$.

Solution

Can anyone spot the projective solution (since I found this in a projective chapter in Lemmas).

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4 Comments

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one million pascals

by wu2481632, Apr 11, 2017, 4:04 PM

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@above: the pressure is on.

by MathAwesome123, Apr 11, 2017, 11:50 PM

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this was in my pascals handout

by cjquines0, Apr 12, 2017, 3:38 PM

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Whoever wrote the last WOOT POTD does not know what concise means (or it just shows my incompetence in hard geo oops sorry Cosmin)

by adik7, Apr 14, 2017, 8:43 PM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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  • Let $ ABC$ be an equilateral triangle of side length $ 1$. Let $ D$ be the point such that $ C$ is the midpoint of $ BD$, and let $ I$ be the incenter of triangle $ ACD$. Let $ E$ be the point on line $ AB$ such that $ DE$ and $ BI$ are perpendicular. $ \

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  • oh my gosh it's been so longggggg.... contrib? what does that mean?

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  • 2019 post

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  • contrib /charmander

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  • for contrib

    by SomethingNeutral, Mar 30, 2017, 7:57 PM

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