Problems(2)
quad inside quad, compare diagonals' sum (2023 Novosibirsk Oral Geo Oly 7.5)
Source:
9/4/2023
One convex quadrilateral is inside another. Can it turn out that the sum of the lengths of the diagonals of the outer quadrilateral is less than the sum of the lengths of the diagonals of the inner?
geometrygeometric inequality
circle inscribed in convex polygon (2023 Novosibirsk Oral Geo Oly 9.5)
Source:
9/5/2023
A circle of length is inscribed in a convex polygon with perimeter . What part of the area of this polygon is occupied by the resulting circle?
geometrypolygon