# Calculate the area of the circle

1. Mar 16, 2013

### Saeed.z

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

any hint ?

thanks

2. Mar 16, 2013

### Ray Vickson

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

3. Mar 16, 2013

### Saeed.z

^

yes, they are length of line segments.

4. Mar 16, 2013

### Staff: Mentor

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

5. Mar 16, 2013

### phinds

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

Last edited: Mar 16, 2013
6. Mar 16, 2013