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Two Crescents (Posted on 2004-08-11) Difficulty: 2 of 5
Given a right triangle, draw the three following semicircles:
  1. The semicircle with diameter formed by one of the legs and extending away from the triangle.
  2. The semicircle with diameter formed by the other leg and extending away from the triangle.
  3. The semicircle with diameter formed by the hypotenuse and extending towards the triangle.

Prove that the area of the two crescents (shown in RED and BLUE) formed by the three semicircles equals the area of the triangle.

No Solution Yet Submitted by ThoughtProvoker    
Rating: 3.2000 (10 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsFolding's too hard.broll2016-02-03 05:17:04
re: I'm I missing something?Vee-Liem Veefessional2010-03-24 02:56:26
I'm I missing something?Axorion2007-11-20 02:30:28
Simple SolutionTim Norwood2006-01-22 13:52:25
Better WrittenCeeAnne2004-10-16 01:38:43
About That Simpler ProofCeeAnne2004-10-13 05:49:14
SolutionSimpler ProofCeeAnne2004-10-11 16:35:37
Too FamiliarCeeAnne2004-09-28 02:14:05
2xElisabeth2004-08-13 21:04:56
SolutionSimpleFederico Kereki2004-08-11 10:52:33
SolutionCutenikki2004-08-11 09:42:35
I like it because...Larry2004-08-11 08:23:27
Questionre: so whatVee-Liem Veefessional2004-08-11 06:57:42
Hints/TipsVehe!Vee-Liem Veefessional2004-08-11 06:50:28
Solutionso whatAdy TZIDON2004-08-11 06:43:06
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