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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021