Calculate the area of the circle

[Saeed.z]

i tried hard to solve this question but i got a complicated answer

any hint ?

http://www.gulfup.net/uploads/13634557771.gif

thanks

 

[Ray Vickson]

i tried hard to solve this question but i got a complicated answer

any hint ?

http://www.gulfup.net/uploads/13634557771.gif

thanks

Show your work.

Anyway, what are the '2' and the '6': are they lengths of line segments, or are they areas of sub-regions?

 

[Saeed.z]

^

yes, they are length of line segments.

 

[Chestermiller]

Label the acute angle θ. Using the right triangle on the bottom, express the radius in terms of θ. Draw a line from the intersection of the secant with the circle arc, running to the intersection of the vertical diameter with the circle arc. This produces another right triangle, with the diameter as its hypotenuse. Express the diameter 2r in terms of θ using this larger triangle.

Chet

 

[phinds]

Label the acute angle θ. Using the right triangle on the bottom, express the radius in terms of θ. Draw a line from the intersection of the secant with the circle arc, running to the intersection of the vertical diameter with the circle arc. This produces another right triangle, with the diameter as its hypotenuse. Express the diameter 2r in terms of θ using this larger triangle.

Chet

Well, I'll take your word for it that that would work, but you sure do like to make things difficult. There is no need to bring angles or trig into it at all. Pythagoras would have gotten this one right off and I don't think he knew any trig.

EDIT: "no need for angles" isn't quite right, since it DOES depend on similar triangles

 

[Chestermiller]

I like your way better, although it gives the same answer.

Chet