# [sf-lug] py class: need math help!

jim jim at well.com
Sun Oct 5 11:14:00 PDT 2008

```i read this as follows:

C center of circle

A and B opposite ends of an arc and
also of the corresponding chord

Eta, the angle ACB

D the midpoint on the arc of AB

E the midpoint of the chord AB

Theta, the value of the two angles ACD and BCD

Therefore, triangles ACE and BCE are similar,
and triangles AED and BED are similar (both
cases are mirror images).
it seems that ACE and AED and BCE and BED
are related in some way, but i don't know how
to express the relationship without thinking,
something i generally avoid.
triangles DAE and DBE share the ED side,
and given the identical length of hypotenuses
DA and DB, then ED is a common sine for the
angles DAE and DBE.
triangles ACE and BCE share the CE side,
and given identical length of hypontenuses
AC and BC (r), then CE is a common cosine
for the angles ACE and BCE.

so what is the goal?

On Sun, 2008-10-05 at 09:47 -0700, Alex Kleider wrote:
>
> I need some help with what seems to be elementary math/trig:
>
> Take a pencil and piece of paper and try to stay with me:
>
> We start at C for center of circle and based on that center
> draw an arc of radius r from A to B such that the angle ACB is equal to twice theta
> bisect our angle with a line from C to D at the midpoint of the arc.
> it intersects AB at E
> Now I've been assuming that triangles DEB and BEC were similar and therefore
> knowing ED and EB I was solving for CB (the radius.)
> i.e : tan theta = ED / EB
>    and radius = CB = EB/sin theta
>
> This is my attempt to solve the next series of problems.
> I'd appreciate any help.
>
>
>
>
>
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```