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Difference between revisions of "1969 IMO Problems/Problem 4"

(Created page with "A semicircular arc <math>\gamma</math> is drawn with <math>AB</math> as diameter. <math>C</math> is a point on <math>\gamma</math> other than <math>A</math> and <math>B</math>...")
(No difference)

Revision as of 14:28, 2 January 2017

A semicircular arc $\gamma$ is drawn with $AB$ as diameter. $C$ is a point on $\gamma$ other than $A$ and $B$, and $D$ is the foot of the perpendicular from $C$ to $AB$. We consider three circles, $\gamma_1, \gamma_2, \gamma_3$, all tangent to the line $AB$. Of these, $\gamma_1$ is inscribed in $\triangle ABC$, while $\gamma_2$ and $\gamma_3$ are both tangent to $CD$ and $\gamma$, one on each side of $CD$. Prove that $\gamma_1, \gamma_2$, and $\gamma_3$ have a second tangent in common.

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