Problems(3)
angle chasing in a figure (2021 Novosibirsk Oral Geo Oly 8.3)
Source:
5/24/2021
Find the angle in the quadrilateral of the figure.
https://cdn.artofproblemsolving.com/attachments/0/2/974e23be54125cde8610a78254b59685833b5b.png
geometryangles
criterion for sides a=2b in a triangle (2021 Novosibirsk Oral Geo Oly 7.3)
Source:
4/27/2021
Prove that in a triangle one of the sides is twice as large as the other if and only if a median and an angle bisector of this triangle are perpendicular
geometryequal segments
perimeter wanted, bisectors _|_ medians (2021 Novosibirsk Oral Geo Oly 9.3)
Source:
5/25/2021
In triangle , side is . It is known that one of the angle bisectors of triangle is perpendicular to one of its medians, and some other angle bisector is perpendicular to the other median. What can be the perimeter of triangle ?
geometryperimeter