MathProblemsBank

5.2.4.25 Various Problems on the Plane

In the correct triangle \ (a b c \) with a side of 12 on the side \ (b c \), a semicircle is built on the diameter that does not have a common point with a triangle \ (a b C \), except for points \ (b \) and \ (C \). It is separated by points \ (a_ {1} \) and \ (a_ {2} \) into three equal arcs \ (b a_ {1} = a_ {1} A_ {2} = A_ {2} C \). Find the lengths of the segments into which the side is divided \ (b c \) straight \ (a_ {1} \) and \ (a_ {2} \).