MathDB
Compute side ratio in triangle if circle passes through incenter

Source: Dutch TST 2024, 3.2

June 28, 2024
ratiogeometrygeometry proposedincenterSides of a triangle

Problem Statement

Let ABCABC be a triangle. A point PP lies on the segment BCBC such that the circle with diameter BPBP passes through the incenter of ABCABC. Show that BPPC=cs−c\frac{BP}{PC}=\frac{c}{s-c} where cc is the length of segment ABAB and 2s2s is the perimeter of ABCABC.
Back to ProblemsView on AoPS