dayum circle problem

N

nanase

Junior Member
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Aug 8, 2019
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circle-geometry-shaded-area.jpg


guys I am having a problem in finding the shaded area,
My strategy is to use subtraction of areas that will eventually lead to shaded area, but I am having problem finding that tiny section that looks like a triangle at the top right and bottom left, any help please
 
I'd do a different subtraction:

FMH120559.png

Subtract the area of the green segment from the area of the blue segment. (A segment of a circle is the region between an arc and a chord.)

Whatever method you use, please show the work you've done, so we can still needs to be done, and suggest changes.
 
Oke let me get thinking, so I will subtract the blue segment with the green segment.
just another question though, how do I get the angles for the blue sector and the green sector??
 
That depends on what you have learned; since you haven't told us the context of the question, or shown specific work, I don't know what to suggest! For example, what do you know of trigonometry? Does this come from a class or contest for which that is expected?

One possibility is to analyze triangle BEK in my picture, all of whose sides are known, using trigonometry (law of cosines). Another might be coordinate geometry.

By the way, what does dayum mean?
 
Hi sir,
It's a unit chapter from our grade 9 topics, we are learning arc and sector in radian.
Interesting suggestion about triangle BEK, I can obtain BE and EK, but how to obtain BK? I can use sine or cosine rule if there is an angle, or pythagoras if it is right-angle triangle, but it is not rite?

for dayum, it's a lingo for damn :)
 
oh my ! haha sorry and thank you ! I missed that one,
one last question sir, how do i get the angle for the blue sector, what I have are only radius EJ=EK=5
 
After a lot of trials and failures, i managed to find the length of chord JK using cosine rule.
I got angle B = 0.97339 radian
chord JK = 9.354
angle E = 2.41886 radian
sector EKHGJ = 30.23575
sector BKJ = 48.6695
triangle BKJ = 41.33987
triangle EKJ = 8.26796
segment KJ = sector BKJ - triangle BKJ = 7.32963
shaded area = sector EKHGJ - segment KJ - triangle EKJ
= 14.63816

fiuh thanks alot dr Peterson, it is your diagram that made me realise that i dont have to worry about subtracting the tiny areas on the top right and bottom left. I can just focus on the inside it self.
thanks a lot. I need to cool down my head now. literally spent hours. ^^
 
Looks good. There are, of course, various ways to carry out the details, but your numbers agree with mine.
 
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