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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: ( Back to comment list | You must be logged in to post comments.)
I'm I missing something? | Comment 13 of 15 |
πa/2 + πb/2 + ab/2 = πc/2 + ab/2

πa/2 + πb/2 = πc/2

a + b = c


  Posted by Axorion on 2007-11-20 02:30:28
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