MathDB

2

Part of 2021 Tuymaada Olympiad

Problems(2)

Tuymaada 2021/ J2

Source: Tuymaada 2021/ J2

7/30/2021
The bisector of angle BB of a parallelogram ABCDABCD meets its diagonal ACAC at EE, and the external bisector of angle BB meets line ADAD at FF. MM is the midpoint of BEBE. Prove that CM//EFCM // EF.
geometry
Trapezoid angle chase

Source: Tuymaada 2021 Senior P2

7/28/2021
In trapezoid ABCDABCD,MM is the midpoint of the base ADAD.Point EE lies on the segment BMBM.It is known that ∠ADB=∠MAE=∠BMC\angle ADB=\angle MAE=\angle BMC.Prove that the triangle BCEBCE is isosceles.
geometry