mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths XI

 Posted on 2014-05-04 

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

Light work

"I don't know if you are fond of puzzles, or not. If you are, try this. ... A gentleman (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it—a square window, 3 feet high and 3 feet wide. Now he had weak eyes, and the window gave too much light, so (don't you like 'so' in a story?) he sent for the builder, and told him to alter it, so as only to give half the light. Only, he was to keep it square—he was to keep it 3 feet high—and he was to keep it 3 feet wide. How did he do it? Remember, he wasn't allowed to use curtains, or shutters, or coloured glass, or anything of that sort."

Show answer & extension

If you enjoyed these puzzles, check out Advent calendar 2024,
puzzles about probability, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025