Construction and Loci - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Construction and Loci.

Printable worksheets containing selections of these problems are available here:

 Stage 4 ★ Sheet 1 Solutions

Pink and White

KS 3 Short Challenge Level:

Weekly Problem 36 - 2013
The white square slides once around the pink square. Through what distance does the point P on the white square move?

Defined Distances

KS 3 Short Challenge Level:

Weekly Problem 51 - 2009
Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

Contact Circles

KS 3 Short Challenge Level:

Weekly Problem 25 - 2010
These four touching circles have another circle hiding amongst them...

Either Side

KS 3 Short Challenge Level:

Weekly Problem 7 - 2012
A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

Folded A4

KS 3 & 4 Short Challenge Level:

Weekly Problem 45 - 2011
What shapes can be made by folding an A4 sheet of paper only once?

Triangular Wheel

KS 4 Short Challenge Level:

Weekly Problem 36 - 2014
An equilateral triangle is rolled along a line. What is the length of the path traced out by one of its vertices?

Pencil Turning

KS 4 Short Challenge Level:

Weekly Problem 37 - 2011
Rotating a pencil twice about two different points gives surprising results...

3-sided

KS 4 Short Challenge Level:

Weekly Problem 9 - 2015
How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?