MathDB

3

Part of 2024 Czech-Polish-Slovak Junior Match

Problems(2)

A funny angle equality in a rigid square configuration

Source: Czech-Polish-Slovak Junior Match 2024, I-3

5/29/2024
Let ABCDABCD be a convex quadrilateral with AB=BD=DCAB=BD=DC and AB⊥BD⊥DCAB \perp BD \perp DC. Let MM be the midpoint of segment BCBC. Show that ∠BAM+∠DCA=45∘\angle BAM+\angle DCA=45^\circ.
geometrygeometry proposed
Subdividing an isosceles triangle in two more

Source: Czech-Polish-Slovak Junior Match 2024, T-3

5/29/2024
Determine the possible interior angles of isosceles triangles that can be subdivided in two isosceles triangles with disjoint interior.
geometrygeometry proposedisoscelesIsosceles Triangle