pop theorem

[canvas]

I have proved the first statement, but I'm really stuck with |AO||BO|=r^2-|OS|^2, using my picture, any hint guys?

 

[Otis]

any hint guys?

Yes. Show us your attempt. (Your sticking point could be as simple as an algebra mistake.)
[imath]\;[/imath]

 

[canvas]

Yes. Show us your attempt. (Your sticking point could be as simple as an algebra mistake.)
[imath]\;[/imath]

The problem is that I

don't even know how to start, I have tried to draw SA and SB like radiuses and use a couple times a pythagorean theorem, but it doesn't give me the result.

I've done it guys!
(1) draw line SO
(2) mark E and F
(3) use proved above theorem for EF and CD
(4) done

 

[Dr.Peterson]

The problem is that I don't even know how to start, I have tried to draw SA and SB like radiuses and use a couple times a pythagorean theorem, but it doesn't give me the result.

View attachment 34274I've done it guys!
(1) draw line SO
(2) mark E and F
(3) use proved above theorem for EF and CD
(4) done

Looks good.

I had to look up "pop theorem" (Power of a Point, which I've heard of by the full name, though it wasn't called that when I learned it), and c.b.d.o. (Co bylo do okazania (Polish: QED))

 

[Steven G]

You should define r and s!! I assume, but shouldn't have to, that s is the center of the circle(?) and that r is the radius of the circle(?). In fact, you never said it was a circle!

 

[Dr.Peterson]

You should define r and S!! I assume, but shouldn't have to, that S is the center of the circle(?) and that r is the radius of the circle(?). In fact, you never said it was a circle!

I presume the reason for this deficiency in the question is that we weren't shown the actual problem at all. I'm willing to make some guesses about students' work, rather than criticize the presentation of a request for help; but I agree it would be better not to have to do that.

@canvas, in the future you should be sure to show us the problem as given to you, so we can be sure what is given (and what is your work). I am guessing that the original was not in English (likely Polish?), but that doesn't prevent you from showing it to us, with a translation as needed.