MathDB

G6

Part of 2024-IMOC

Problems(1)

Difficult Geometry in 2024 IMOC

Source: 2024 imocsl G6 (Night 4-G)

8/8/2024
ABCDABCD is a cyclic quadrilateral and ACAC intersects BDBD at EE. M,NM, N are the midpoints of AB,CDAB, CD, respectively. ⊙(AMN)\odot(AMN) meets ⊙(ABCD)\odot(ABCD) again at PP. ⊙(CMN)\odot(CMN) meets ⊙(ABCD)\odot(ABCD) again at QQ. ⊙(PEQ)\odot(PEQ) meets BDBD again at TT. Prove that M,N,TM,N,T are colinear.
Proposed by chengbilly
geometryIMOC