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# Previous Puzzles of the Month + Solutions

May-June 2009, Puzzle nr 121
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Puzzle # 121 Difficulty level: , general math knowledge.

 Circle vs Square    The diameter a of the large semicircle below is 10 cm long. Knowing that one of the vertices of the square meets the circumference of the small circle at point P (see diagram above), try to guess the area of the blue square WITHOUT using trigonometry! Keywords: sangaku, tangent property, bisector theorem. Related puzzles: - Perpendicular or not? - Ratio of similar triangles. - Area incognita Il diametro a del semicerchio qui sopra vale 10 cm; sapendo che un vertice del quadrato (punto P) appartiene anche alla circonferenza piccola, qual è l'area del quadrato? È vietato utilizzare la trigonometria per risolvere questo problema! Parole chiave: sangaku. Suggerisci un'altra soluzione Chiudi - La surface X Le diamètre a du demi-cercle ci-dessus vaut 10 cm; sachant qu'un des sommets du carré (point P) appartient aussi à la circonférence du petit cercle, peux-tu nous dire quelle est l'aire du carré bleu? Il est interdit d'utiliser la trigonométrie pour résoudre ce problème! Mots clés: sangaku. Propose une autre solution Fermer Source of the puzzle: BrainTrainer, issue #23. © G. Sarcone. You cannot reproduce any part of this page without prior written permission.

 More Math Facts behind the puzzle Angle bisector and proportions If a segment bisects an angle of a triangle then it divides the two segments on either side proportionally: CA / CP = BA / PB and CA x PB = CP x BA Angle bisector theorem on Wikipedia.

Previous puzzles of the month...
 Jan-Feb 09: Geometric mouse Sept-Oct 08: perpendicular or not... July-Aug 08: ratio of triangles May-June 08: geometry of the bees Febr-March 08: parrot sequence... Dec 07-Jan 08: probable birthdates? Oct-Nov 2007: infinite beetle path Aug-Sept 07: indecisive triangle June-July 07: Achtung Minen! April-May 07: soccer balls Febr-March 07: prof Gibbus' angle Jan 07: triangles to square Aug-Sept 2006: balance problem June-July 06: squared strip Apr-May 06: intriguing probabilities Febr-March 06: cows & chickens Dec 05-Jan 06: red monad Sept-Oct 2005: magic star July-Aug 05: cheese! May 05: stairs to square Febr 05: same pieces Sept-Oct 2004: odd triangles Puzzle Archive More Puzzles

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