FUN GEOMETRY PROBLEM | MATH OLYMPIAD
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- Опубликовано: 21 апр 2024
- The marked point is the center of the larger semicircle
Learn how to find the area of the green shaded semicircle. Important Geometry and skills are also explained: area of a square formula; similar triangles; area of a triangle formula; Pythagorean Theorem; and right triangles. Step-by-step tutorial by FA_Math
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This is a nice problem, but it would help those of us who want to work it out for ourselves if you would make it explicit in the drawing that the radius of green circle is exactly half the radius of the large outer circle. It appears that way, but it would be helpful to indicate it explicitly in the figure.
If you look carefully, the center of the larger semicircle is marked
@@FA_Math I have the same objection as SanePerson1. It should be explicitly stated that the marked point is the center of the larger semicircle, or that the ratio of diameters is 2:1.
My kids have just learnt about simultaneous equations and the heavy algebra that goes along with it.
This will make such an awesome "try and get the same answer" exercise!
The problem seems so "elegant" at first, then the Algebra creeps in...
Nice
Thanks
Nice work! Keep uploading geometry problems! I came up with the same solution. I 'll try if i can figure out another different.
Many thanks ❤️
First Radius of the big semi circle will be equal to the diameter of the smaller semi circle
Second we know that the radius of the circle inside the bigger semicircle is 1 uni..
Then radius of the bigger semi cicle will be 1 + 1root2
Then as I told that the radius of the bigger semi circle is = to the diameter of the smaller semicircle and the radius of the small semicircle is = the radius of the big semicircle divided by 2. we know that the area of a semicircle is (pir^2)/2
As radius of the bigger semicircle is equal to the diameter of the smaller semicircle
After putting the values we get the area of the green shaded region or the area of the small semicircle is equal to 2.288....unit square😊😊😊😊😊
(Because ,If form a square in the circle the side length of the square will be 1 as well and the diagonal will be 1root 2).
How exciting!
Thank you so much ❤️