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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!

Please share your answer to view other submitted answers
Parents
  • The area of the portion of blue circle B that is situated outside circle R is 8 sq cm.

    Complete the square inside the circle.  The circle B radius is half the diagonal of the square or sqrt(8).

    Each segment of B with cord length of 4cm has an area of (2PI-4) sq cm.

    The quarter circle area is 4PI sq cm

    The circle B area is 8PI

    Area of B outside is equal to 8PI - 4PI - 2*(2PI-4) = 8 sq cm.

Reply
  • The area of the portion of blue circle B that is situated outside circle R is 8 sq cm.

    Complete the square inside the circle.  The circle B radius is half the diagonal of the square or sqrt(8).

    Each segment of B with cord length of 4cm has an area of (2PI-4) sq cm.

    The quarter circle area is 4PI sq cm

    The circle B area is 8PI

    Area of B outside is equal to 8PI - 4PI - 2*(2PI-4) = 8 sq cm.

Children