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


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


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