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


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


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