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A, I, P, Q concyclic wanted, AD+AE=BC, circle passing through B,C
parmenides51   0
Nov 28, 2022
Source: 2010 JJMO p4 - Junior Japan Math Olympiad Finals
Given a triangle $ABC$. A circle $\omega$ passing through points $B$ and $C$, intersects line segments $AB$ and $AC$ (not including endpoints) at points $D$ and $E$, respectively, and $AD+AE=BC$ holds. Let $I$ be the incenter of the triangle $ABC$. Let $P$ and $Q$ be the points, other than $B,C$ , where the straight lines $BI$ and $CI$ intersect the circle $\omega$ . Show that $A, I, P$ and $Q$ lie on the same circle.
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parmenides51
Nov 28, 2022
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A, I, P, Q concyclic wanted, AD+AE=BC, circle passing through B,C
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Source: 2010 JJMO p4 - Junior Japan Math Olympiad Finals
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parmenides51
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Given a triangle $ABC$. A circle $\omega$ passing through points $B$ and $C$, intersects line segments $AB$ and $AC$ (not including endpoints) at points $D$ and $E$, respectively, and $AD+AE=BC$ holds. Let $I$ be the incenter of the triangle $ABC$. Let $P$ and $Q$ be the points, other than $B,C$ , where the straight lines $BI$ and $CI$ intersect the circle $\omega$ . Show that $A, I, P$ and $Q$ lie on the same circle.
This post has been edited 2 times. Last edited by parmenides51, Nov 28, 2022, 1:38 PM
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