2

Part of 2019 Oral Moscow Geometry Olympiad

Problems(2)

parallelogram on side of a triangle, concurrent lines wanted

Source: 2019 Oral Moscow Geometry Olympiad grades 8-9 p2

AC

of the triangle

ABC

in the external side is constructed the parallelogram

ACDE

O

be the intersection point of its diagonals,

N

K

be midpoints of BC and BA respectively. Prove that lines

DK, EN

BO

intersect at one point.

geometryparallelogramconcurrencyconcurrent

quadrilateral with same angles, equal diagonals, are equal?

Source: 2019 Oral Moscow Geometry Olympiad grades 10-11 p2

The angles of one quadrilateral are equal to the angles another quadrilateral. In addition, the corresponding angles between their diagonals are equal. Are these quadrilaterals necessarily similar?

congruentquadrilateraldiagonalscongruencegeometry