MathDB

12

Part of 2022 MMATHS

Problems(2)

2022 MMATHS Team Online p12 - 5th and final geo on the test, long live geo

Source:

10/1/2023
Let triangle ABCABC with incenter II satisfy AB=3AB = 3, AC=4AC = 4, and BC=5BC = 5. Suppose that DD and EE lie on ABAB and ACAC, respectively, such that DD, II, and EE are collinear and DE⊥AIDE \perp AI. Points PP and QQ lie on side BCBC such that IP=BPIP = BP and IQ=CQIQ = CQ, and lines DPDP and EQEQ meet at SS. Compute SI2SI^2.
geometryMMATHS
2022 MMATHS Individual p12 - Geometry, where art thou?

Source:

10/1/2023
Let triangle ABCABC with incenter II satisfy AB=10AB = 10, BC=21BC = 21, and CA=17CA = 17. Points DD and E lie on side BCBC such that BD=4BD = 4, DE=6DE = 6, and EC=11EC = 11. The circumcircles of triangles BIEBIE and CIDCID meet again at point PP, and line IPIP meets the altitude from AA to BCBC at XX. Find (DX⋅EX)2(DX \cdot EX)^2.
geometryMMATHS