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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 origin of circle B is half distance of line OM and ON, therefore 2cm from O.  Radius of circle B is a^2+b^2=r^2 = sqrt(8).  

    quarter of the circle R is 4^2*pi/4=12.566

    The areas of arc MO and NO can be found by taking 1/2 area of circle B minus area of triangle MNO.  Therefore = 4.566

    The total Intersect area of circle R and B would be  12.566+4.566= 17.133cm^2    <------HERE I REALIZE I CALCULATED THE INTERSECTED AREA

    So the Outer Area would be Area circle B minus the Inside Intersect which is 8cm^2

     

Reply
  • The origin of circle B is half distance of line OM and ON, therefore 2cm from O.  Radius of circle B is a^2+b^2=r^2 = sqrt(8).  

    quarter of the circle R is 4^2*pi/4=12.566

    The areas of arc MO and NO can be found by taking 1/2 area of circle B minus area of triangle MNO.  Therefore = 4.566

    The total Intersect area of circle R and B would be  12.566+4.566= 17.133cm^2    <------HERE I REALIZE I CALCULATED THE INTERSECTED AREA

    So the Outer Area would be Area circle B minus the Inside Intersect which is 8cm^2

     

Children