MathDB
concurrency wanted, cyclic ABCD, 4 more circles related

Source: Mathley 2014.2 p5

August 20, 2020
geometryCycliccircles

Problem Statement

A quadrilateral ABCDABCD is inscribed in a circle (O)(O). Another circle (I)(I) is tangent to the diagonals AC,BDAC, BD at M,NM, N respectively. Suppose that MNMN meets AB,CDAB,CD at P,QP, Q respectively. The circumcircle of triangle IMNIMN meets the circumcircles of IAB,ICDIAB, ICD at K,LK, L respectively, which are distinct from II. Prove that the lines PK,QLPK, QL, and OIOI are concurrent.
Tran Minh Ngoc, a student of Ho Chi Minh City College, Ho Chi Minh
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