Thread: [SOLVED] semi-circle

hi everyone
please could someone help me with a problem. If i have a semi-circle, and at the baseline , at certain intervals on that baseline, i need to know what the height is to the arc of the semi-circle , at right angles to the baseline , would anyone have a formula i could use

cheers

Hello, dnoster!

I have a semicircle, and at certain intervals on the diameter, I have points.
I need to know the height from the points to the arc of the semicircle.

Code:

          C
          * * *
        */: \     *
      * / :   \     *
     * /  :     \    *
      /   :h      \
    */    :         \ *
    *-----*--+--------*
    A  x  P   2r-x    B

A triangle inscribed in a semicircle is a right triangle: .

We have a point on the diameter, where

If is the radius of the circle, then


. . . . . . . . . . . . . . . . . Theorem
. . . . . The altitude to the hypotenuse of a right triangle
. . . . . . . . . . . . .is the mean proportional
. . . . . . . . of the two segments of the hypotenuse.


That is: .

Therefore: .

Originally Posted by dnoster

hi everyone
please could someone help me with a problem. If i have a semi-circle, and at the baseline , at certain intervals on that baseline, i need to know what the height is to the arc of the semi-circle , at right angles to the baseline , would anyone have a formula i could use cheers

Hello,

here is another way to do your problem:
Let the center of your circle be the origin of a coordinate system. Then you can use the Pythagorian theorem:

x-value = b
height to the arc of the semi-circle = a

Then you get:



I've attached a diagram to show what I've calculated.

Greetings

EB