Construction of a triangle
Source: 2019-20 International's Dürer Competition, Category E+,P4
August 19, 2020
geometryConstruct
Problem Statement
Suppose that you are given the foot of the altitude from vertex of a scalene triangle , the midpoint of the arc with endpoints and , not containing of the circumscribed circle of , and also a third point . Construct the triangle from these three points if is the
a) orthocenter
b) centroid
c) incenter
of the triangle.