9.3
Problems(3)
angle wanted, 1 circles and 3 lines (II Soros Olympiad 1995-96 R1 9.3)
Source:
6/2/2024
Two straight lines are drawn on a plane, intersecting at an angle of . A circle with center at point touches these lines. Let's consider a line, different from the given ones, tangent to the same circle and intersecting the given lines at points and . What can the angle be equal to?
geometryangles
convex pentagon, diagonal = side (II Soros Olympiad 1995-96 R2 9.3)
Source:
6/3/2024
Is there a convex pentagon in which each diagonal is equal to some side?
geometrycombinatorial geometrypentagon
4 different right triangles from 5 segments (II Soros Olympiad 1995-96 R3 9.3)
Source:
6/4/2024
It is known that from these five segments it is possible to form four different right triangles. Find the ratio of the largest segment to the smallest.
combinatoricscombinatorial geometrygeometry