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MathNet 2010 — Part 02 Question 115

Math Olympiad Vault · MathNet 2010 — Part 02

Question 115

Be $g$ One straight in the plane. the circles $k_{1}$ and $k_{2}$ lie on the same page of $g$ and touch $g$ in the points $A$ respectively $B$. Another circle $k_{3}$ touch $k_{1}$ in $D$ and $k_{2}$ in $C$. Prove that applies:

(a) the square $A B C D$ is a quadrilateral.

(b) The straight lines $B C$ and $A D$ cut themselves on $k_{3}$.