Given a semicircle and a green circle inside a quarter circle, find the area of the green circle.

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Find the area of the green circle by drawing triangles and using the Pythagorean Theorem.
  1. The Math District
  2. geometry
  3. triangle
  4. right triangle
  5. Pythagorean theorem
  6. quarter circle
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Автор

تمرين جميل جيد . رسم واضح مرتب . شرح واضح مرتب. شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم . تحياتنا لكم من غزة فلسطين .

اممدنحمظ
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Can it be assumed, or better yet proven, that triangle ABO is is an isosceles triangle ? If that is the case then 8+x = 16-x and we can skip all of the fancy algebra. You just demonstrated that in this particular case it is.

larrydickenson
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what if you would place a third circle that is tangent to green circle, diameter of the quarter circle and the edge of the quarter circle. What would the radius be of that smaller circle?

tgrgt
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Seems you could go faster, assuming that ABO is an isocele triangle, AB=OB, so 8+x=16-x and you find that x=4. But how can you prove it first?

MrMichelX
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Green circle radius = r/4 = 16/4 = 4
Then it's Area = πr² = 16π
Add on :- Pink circle radius = r/2 = 16/2= 8

amitanand
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It looks better to stop at BE^2 and avoid estimating BE and than squaring it twice, i.e. final equation should be BE^2(AEB)=BE^2(OEB).
Thumb up any case.

michaelkouzmin