Need help to find point E so that area of X equals area of Y.

[rva]

Draw a segment from E to any point between I and K so that areas X and Y maked in red and green will be equal.
In this example over here i have drawn segment from E to G however i don't think that over here X = Y.

 

[khansaheb]

Draw a segment from E to any point between I and K so that areas X and Y maked in red and green will be equal.
In this example over here i have drawn segment from E to G however i don't think that over here X = Y.

View attachment 36851

What are the points J,K,I, H, F, etc. ?

What are the unknowns (variables) of this problem?

Now from the given information in the problem, set up the equation.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[Dr.Peterson]

Draw a segment from E to any point between I and K so that areas X and Y maked in red and green will be equal.
In this example over here i have drawn segment from E to G however i don't think that over here X = Y.

View attachment 36851

I think your title is wrong; E is a known point. Is it G that you want to find?

Please state the entire problem exactly as given to you. What is the significance of I and K?

I would probably want to name the point (L?) where line k intersects the arc, and express its location in terms of some variable (the y-coordinate of G?), and use that to work out the area of the circular segment "X". Area "Y" might be calculated from a circular segment and a triangle.

What formulas have you learned or looked up? Or do you know enough calculus to do this? (Not necessarily a recommended method.)