MathDB

2

Part of 2022 239 Open Mathematical Olympiad

Problems(2)

Problem 2

Source: 239-School Open Olympiad (Senior Level)

4/25/2022
Five edges of a tetrahedron are tangent to a sphere. Prove that there are another five edges from this tetrahedron that are also tangent to a ((not necessarily the same)) sphere.
3D geometrySpheresgeometry
Geometry with circumscribed quadrilateral

Source: 239-School Open Olympiad 2022, Junior League P2

4/19/2023
Point II{} is the center of the circle inscribed in the quadrilateral ABCDABCD. Prove that there is a point KK{} on the ray CICI such that ∠KBI=∠KDI=∠BAI\angle KBI=\angle KDI=\angle BAI.
geometryincircle