Cutting corners

The diagram below shows a triangle \(ABC\). The line \(CE\) is perpendicular to \(AB\) and the line \(AD\) is perpedicular to \(BC\).
The side \(AC\) is 6.5cm long and the lines \(CE\) and \(AD\) are 5.6cm and 6.0cm respectively.
How long are the other two sides of the triangle?

Show answer

Equal side and angle

In the diagram shown, the lengths \(AD = CD\) and the angles \(ABD=CBD\).
Prove that the lengths \(AB=BC\).

Show answer


Prove that \(\arctan(1)+\arctan(2)+\arctan(3)=\pi\).

Show answer & extension


A sine curve can be created with five people by giving the following instructions to the five people:
A. Stand on the spot.
B. Walk around A in a circle, holding this string to keep you the same distance away.
C. Stay in line with B, staying on this line.
D. Walk in a straight line perpendicular to C's line.
E. Stay in line with C and D. E will trace the path of a sine curve as shown here:
What instructions could you give to five people to trace a cos(ine) curve?
What instructions could you give to five people to trace a tan(gent) curve?

Show answer & extension

arccos + arcsin

What is the value of \(\arccos(x) + \arcsin(x)\)?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


sums advent clocks quadratics square roots coins algebra 3d shapes division remainders crossnumber chess indices people maths polygons arrows complex numbers symmetry numbers gerrymandering digits folding tube maps taxicab geometry differentiation factorials irreducible numbers triangles partitions spheres square numbers sum to infinity money hexagons number proportion lines elections shapes games speed coordinates area palindromes logic means perfect numbers rectangles integration crosswords chalkdust crossnumber grids sequences range percentages angles dodecagons crossnumbers regular shapes floors factors routes balancing calculus functions parabolas books cryptic crossnumbers multiplication tiling sport trigonometry ave graphs probability median multiples triangle numbers doubling geometry ellipses rugby colouring dominos planes squares addition cryptic clues shape scales menace pascal's triangle probabilty products dates circles cube numbers surds wordplay christmas mean averages star numbers time chocolate odd numbers integers prime numbers 2d shapes fractions cards digital clocks volume dice bases the only crossnumber unit fractions perimeter


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020