# Comparing Incircles

Geometry Level 4

A triangle $$ABC$$ has incentre $$I$$. Consider lines $$l_a$$ passing through $$A$$, $$l_b$$ passing through $$B$$ and $$l_c$$ passing through $$C$$ and respectively parallel to sides $$BC$$, $$CA$$ and $$AB$$. By the intersections of these lines, we obtain a triangle $$\Delta_1$$.

Now, reflect the line $$l_a$$ across line $$AI$$ to obtain line $$L_a$$, reflect the line $$l_b$$ across line $$BI$$ to obtain line $$L_b$$ and reflect the line $$l_c$$ across line $$CI$$ to obtain line $$L_c$$. By the intersections of these new lines, we obtain a triangle $$\Delta_2$$.

Then the correct relationship is:

(* Definitions: The reflection of a point $$P$$ across a line $$l$$ is another point $$P'$$ such that $$l$$ is the perpendicular bisector of segment $$PP'$$. The reflection of a line $$l_x$$ across a line $$l$$ is another line $$L_x$$ such that the reflection of each point of $$l_x$$ across line $$l$$ lies on $$L_x$$.)

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