Shortcuts

 Sitemap Contact Newsletter Store Books Features Gallery E-cards Games

 ••• Related links Puzzles workshops for schools & museums. Editorial content and syndication puzzles for the media, editors & publishers. Abracada-Brain Teasers and Puzzles! Numbers, just numbers... Have a Math question? Ask Dr. Math! ••• ••• Logic smile! If you want to build a ship don't herd people together to collect wood and don't assign them tasks and work, but rather teach them to long for the endless immensity of the sea...      - A. Saint-Exupery Original text: Si tu veux construire un bateau, ne rassemble pas des hommes pour aller chercher du bois, préparer des outils, répartir les taches, alléger le travail, mais enseigne aux gens la nostalgie de l’infini de la mer...      - A. Saint-Exupery ••• SPACE INVADERS Play Space Invaders online!

# Previous Puzzles of the Month + Solutions

September-October 2008, Puzzle nr 119
Back to Puzzle-of-the-Month page | Home

Puzzle # 119 Difficulty level: , general math knowledge.

 Perpendicular or not?   The large circle (O1, B) above circumscribes 2 smaller circles (with centers O2 and O3, respectively) and an isosceles triangle, whose base stands on the diameter of the large circle. As shown in the drawing, each geometric shape touches the 3 other ones. Points A, O1, O2 and B are aligned. Demonstrate that the segment O3A is perpendicular to the diameter AB. Keywords: incircles, isosceles, perpendicular, secant-tangent. Related puzzles: - Ratio of similar triangles. - Soccer ball problem. - Ad angolo retto? Il grande cerchio (O1, B) circoscrive 2 cerchi minori (con i rispettivi centri O2 e O3) e un triangolo isoscele, la cui base si confonde col diametro del grande cerchio. Ogni figura geometrica tocca ognuna delle altre tre. I punti A, O1, O2 e B sono allineati. Dimostrare che il segmento O3A è perpendicolare al diametro AB. Parole chiave: cerchio inscritto, isoscelo, perpendicolare. Suggerisci un'altra soluzione Chiudi - A angle droit? Le grand cercle (O1, B) circonscrit 2 autres cercles plus petits (ayant pour centres O2 et O3, respectivement) ainsi qu’un triangle isocèle, dont la base se trouve sur le diamètre du grand cercle. Chaque figure géométrique touche les 3 autres. Les points A, O1, O2 et B sont alignés. Démontrer que le segment O3A est bien perpendiculaire au diamètre AB. Mots clés: cercle inscrit, isocèle, perpendiculaire. Propose une autre solution Fermer Source of the puzzle: Sangaku tablet of Gunma prefecture (群馬県; Gunma-ken), 1803. ©G. Sarcone.

 More Math Facts behind the puzzle Secant-tangent theorem: fig. 1) c2 = a(a + b) and fig. 2) c2 = a(a + 2r) The angle, formed between a tangent line and a chord, is congruent to the inscribed angle on the other side of the chord and subtended by the chord (angle α' = angle α, see fig. 3). Then, with similar triangles: c / (a + b) = a / c

Back to Puzzle-of-the-Month page | Home