MathDB

G2

Part of 2021 Romanian Master of Mathematics Shortlist

Problems(1)

Geometry is objectively cooler when "it turns out that"

Source: RMM Extralist 2021 G2

9/18/2023
Let ABCABC be a triangle with incenter II. The line through II, perpendicular to AIAI, intersects the circumcircle of ABCABC at points PP and QQ. It turns out there exists a point TT on the side BCBC such that AB+BT=AC+CTAB + BT = AC + CT and AT2=ABā‹…ACAT^2 = AB \cdot AC. Determine all possible values of the ratio IP/IQIP/IQ.
geometryRMM ShortlistInversionsimilaritiesBashingincentercircumcircle