MathDB

6

Part of 2024 Tuymaada Olympiad

Problems(2)

CM \perp DN

Source: Tuymaada 2024 Juniors P6

7/10/2024
Extension of angle bisector BLBL of the triangle ABCABC (where AB<BCAB < BC) meets its circumcircle at NN. Let MM be the midpoint of BLBL. Isosceles triangle BDCBDC with base BCBC and angle equal to ABCABC at DD is constructed outside the triangle ABCABC. Prove that CM⊥DNCM \perp DN. Proposed by А. Mardanov
geometry
Tuymaada 2024 Senior P6

Source: Tuymaada 2024 Senior league P6

7/9/2024
The triangle ABCABC is given. On the arc BCBC of its circumscribed circle, which does not contain point AA, the variable point XX is selected, and on the rays XBXB and XCXC, the variable points YY and ZZ, respectively, so that XA=XY=XZXA = XY = XZ. Prove that the line YZYZ passes through a fixed point. Proposed by A. Kuznetsov
geometry