Can you construct the incenter of a triangle ABC?
Source: 2023 Girls in Mathematics Tournament- Level B, Problem 4
October 29, 2023
geometryincenter
Problem Statement
Given points and , Jaqueline has a ruler that allows tracing the line . Jaqueline also has a special object that allows the construction of a circle of diameter . Also, always when two circles (or a circle and a line, or two lines) intersect, she can mark the points of the intersection with a pencil and trace more lines and circles using these dispositives by the points marked. Initially, she has an acute scalene triangle . Show that Jaqueline can construct the incenter of .