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KCC's Quizzes AQQ258 about a partial eclipse Sun-Moon

1. Quote of the week: "People say nothing is impossible; but I do nothing every day!" - Anonymous

                     

2. New quiz: AQQ258 about a partial eclipse Sun-Moon

     

Some of us (in Dallas) had probably the chance to have observed a total eclipse of the Sun last week.

To celebrate that event in our quizzes, we propose the following related challenge: 

The above pictures describe a partial eclipse between the moon (circle B) and the sun (circle R).

At a certain instant, the eclipse is such that points MNO form a quarter area of circle R; meaning arc MN is a quarter circle).

At that moment, point O is the center of R and the segment OM measures 4 cm.

Question:

What is the area of the portion of blue circle B that is situated outside circle R?

Good luck! And try to be among the firsts!

Kuo-Chang

P.S. Don't hesitate to share those weekly quizzes in EZ to colleagues or friends!

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  • Answer is 8cm2

    SInce the circumf. angle is PI/2, the segment connecting M and N is a diameter of B. You can then calculate radius of B by using Pitagora, r= 2*sqrt (2).Let's call C the portion of circle B we're looking for. This is equal to half of the area of B (you can easily calculate that as you know radius r) minus the area A of the circular segment identified by M, N and the diameter connecting these two points. The area A is equal to a quarter of the area of R minus the area of the triangle OMN. With some calculation you get C= 8cm2

  • Correct Gaetano! Congratulation!

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