Problems(3)
are these triangles always congruent ? (2021 Novosibirsk Oral Geo Oly 7.4)
Source:
4/27/2021
It is known about two triangles that for each of them the sum of the lengths of any two of its sides is equal to the sum of the lengths of any two sides of the other triangle. Are triangles necessarily congruent?
angles
angle wanted, angle bisectors given (2021 Novosibirsk Oral Geo Oly 8.4)
Source:
5/24/2021
Angle bisectors and are drawn in triangle . It turned out that is the bisector of triangle . Find the angle .
geometryangle bisectorangles
tangent semicircle and 1/4 circle in square (2021 Novosibirsk Oral Geo Oly 9.4)
Source:
5/25/2021
A semicircle of radius and a quarter of a circle of radius touch each other and are located inside the square as shown in the figure. Find the length of the part of the common tangent, enclosed in the same square.
https://cdn.artofproblemsolving.com/attachments/f/2/010f501a7bc1d34561f2fe585773816f168e93.png
tangent circlesgeometrysquare