2

Part of 2019 Federal Competition For Advanced Students, P1

Problems(1)

equal segments wanted, circles passing through incenter related

Source: 2019 Austrian Federal Competition For Advanced Students, Part 1 p2

ABC

be a triangle and

I

its incenter. The circle passing through

Y

I

intersect the line

BC

for second time at point

X

. The circle passing through

B, C

I

intersects the line

AC

for second time at point

Y

. Show that the segments

AY

BX

have equal length.

geometryincentercirclesequal segments