Skip to main content
Links to the University of Cambridge website
Links to the NRICH website Home page
Nurturing young mathematicians: teacher webinars
30 April (Primary)
,
1 May (Secondary)
menu
search
Teachers
expand_more
Early years
Primary
Secondary
Post-16
Events
Professional development
Students
expand_more
Primary
Secondary
Post-16
Parents
expand_more
Early Years
Primary
Secondary
Post-16
Problem-solving Schools
About NRICH
expand_more
About us
Impact stories
Support us
Our funders
Contact us
search
Site search
search
Or search by topic
Number and algebra
The Number System and Place Value
Calculations and Numerical Methods
Fractions, Decimals, Percentages, Ratio and Proportion
Properties of Numbers
Patterns, Sequences and Structure
Algebraic expressions, equations and formulae
Coordinates, Functions and Graphs
Geometry and measure
Angles, Polygons, and Geometrical Proof
3D Geometry, Shape and Space
Measuring and calculating with units
Transformations and constructions
Pythagoras and Trigonometry
Vectors and Matrices
Probability and statistics
Handling, Processing and Representing Data
Probability
Working mathematically
Thinking mathematically
Mathematical mindsets
For younger learners
Early Years Foundation Stage
Advanced mathematics
Decision Mathematics and Combinatorics
Advanced Probability and Statistics
Mechanics
Calculus
Two Points Plus One Line
Age
14 to 16
Challenge Level
Problem
Getting Started
Student Solutions
Teachers' Resources
Simple hint: how would you find the set of points that are equidistant from two given points?
When might that locus not intersect with the given line?
Harder, last part: try dropping perpendiculars from $A$ and $B$ onto the given line.
The distance between those positions might be useful.
When is $P$ between those positions and when is it outside?