Click here to win prizes by solving the puzzle Advent calendar.
Click here to win prizes by solving the puzzle Advent calendar.



Semi circle in a triangle

This right-angled triangle above has sides of lengths 12cm, 5cm and 13cm. The diameter of the semicircle lies on the 12cm side and the 13cm side is a tangent to the circle. What is the radius of the semi circle?

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths XI,
puzzles about 2d shapes, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2019