Geometry -> Right Triangles

A focused counting-geometry subtopic around perpendicular vectors, normalized slopes, and pivot-based counting.

• Topic slug: geometry/right-triangles
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 1
• Repo companion pages: 0
• Curated external problems: 5

Microtopics

• right-angle detection
• normalized-slope
• perpendicular-vectors
• pivot-counting
• integer-geometry
• direction-bucketing

Learning Sources

Source	Type
cp-algorithms basic geometry	Reference
cp-algorithms oriented area	Reference
Princeton geometric primitives	Course

Practice Sources

Source	Type
CSES Point Location Test	Practice
CSES Polygon Area	Practice
USACO contest archive	Practice

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Triangle	Codeforces	Easy	Classification	-	-	Distance-Checks; Integer-Grid; Right-Angle	A small but useful right-triangle recognition/classification task.
Pythagorean Triples	Codeforces	Medium	Number Theory	-	-	Integer-Sides; Construction; Pythagorean	Directly about right triangles and integer side lengths.
Right Triangles	Codeforces	Medium	Grid-Counting	Counting	Row/Column Counts	Combinatorics; Orthogonal; Stars-Grid	The standard orthogonal grid right-triangle counting problem.
Triangle	Codeforces	Medium	Construction	-	-	Integer-Coordinates; Existence; Coordinate-Geometry	Constructing a right triangle with integer coordinates is core practice.

Challenge

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Lovely Perfect Right Triangles	Codeforces Gym	Hard	-	Enumeration; Number Theoretic Filtering	Pythagorean Triples; GCD	Number Theory; Counting	A harder right-triangle counting task with strong arithmetic structure.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
PRAVO	Tam giác vuông	primary	medium	count right triangles; normalized directions; perpendicular pairing	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py