Question 186
Suppose for a triangle $ABC$ the following condition is satisfied:
A circle $O$ going through the vertices $B, C$ intersects the line segments $AB$ and $AC$ (excluding the end-points) at the points $D$ and $E$, respectively, and $AD + AE = BC$ is satisfied.
Let $I$ be the in-center of the triangle $ABC$ and suppose that the lines $BI$ and $CI$ intersect the circle $O$ at $P, Q$ (different from $B, C$), respectively. Prove that the points $A, I, P, Q$ lie on the same circumference of a circle.
Here by $XY$ we mean the length of the line segment $XY$.
A circle $O$ going through the vertices $B, C$ intersects the line segments $AB$ and $AC$ (excluding the end-points) at the points $D$ and $E$, respectively, and $AD + AE = BC$ is satisfied.
Let $I$ be the in-center of the triangle $ABC$ and suppose that the lines $BI$ and $CI$ intersect the circle $O$ at $P, Q$ (different from $B, C$), respectively. Prove that the points $A, I, P, Q$ lie on the same circumference of a circle.
Here by $XY$ we mean the length of the line segment $XY$.