MathDB

2

Part of 2020 Stanford Mathematics Tournament

Problems(2)

SMT 2020 Geometry #2

Source:

8/9/2023
Let △ABC\vartriangle ABC be a right triangle with ∠ABC=90o\angle ABC = 90^o. Let the circle with diameter BCBC intersect ACAC at DD. Let the tangent to this circle at DD intersect ABAB at EE. What is the value of AEBE\frac{AE}{BE} ?
geometry
SMT 2020 Geometry Tiebreaker #2 3D

Source:

8/9/2023
On each edge of a regular tetrahedron, five points that separate the edge into six equal segments are marked. There are twenty planes that are parallel to a face of the tetrahedron and pass through exactly three of the marked points. When the tetrahedron is cut along each of these twenty planes, how many new tetrahedrons are produced?
geometry3D geometry