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 geometry, or a random puzzle.


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


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


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