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Sharygin Geometry Olympiad
2023 Sharygin Geometry Olympiad
3
3
Part of
2023 Sharygin Geometry Olympiad
Problems
(1)
maximum diameter less than medial line
Source: Sharygin 2023 - P3 (Grade-8)
3/4/2023
A circle touches the lateral sides of a trapezoid
A
B
C
D
ABCD
A
BC
D
at points
B
B
B
and
C
C
C
, and its center lies on
A
D
AD
A
D
. Prove that the diameter of the circle is less than the medial line of the trapezoid.
geometry
trapezoid
Sharygin Geometry Olympiad
Sharygin 2023