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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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Parents
  • The are of the portion that is outside will be 8

    If sun center is o meaning mo is radius that is 4 and on will also become 4, area of triangle will become 1/2*4*4 that is 8 and quarter area of sun is pi*4*4/4 that is 4*pi so the area of arc mn excluding traingle will be 4"pi -8 and area of half circle moon will be 4*pi with radius 2 sqrt(2) and so 4*pi-(4*pi-8) 

    And hence the arc that is outside with have area of 8

Reply
  • The are of the portion that is outside will be 8

    If sun center is o meaning mo is radius that is 4 and on will also become 4, area of triangle will become 1/2*4*4 that is 8 and quarter area of sun is pi*4*4/4 that is 4*pi so the area of arc mn excluding traingle will be 4"pi -8 and area of half circle moon will be 4*pi with radius 2 sqrt(2) and so 4*pi-(4*pi-8) 

    And hence the arc that is outside with have area of 8

Children