New member ask for help via pm

[jonah2.0]

Beer soaked ramblings follow.
Just received the following pm from new member stefanie:



I'm not exactly sure why this young lady chose me among more capable helpers out here to help her out.
Maybe my Don Quixote avatar gives the impression of a kindly old man.
At any rate, I thought perhaps I'd share her little problem with the rest of the FMH community.
My main issue with this problem is that it wasn't stated explicitly if the line from C to D is a tangent line.
If it really is a tangent line then the problem becomes a conditional equation involving Pythagoras' theorem.
I guess we're just gonna have to wait for her confirmation about the tangent line situation and her response to my hint.

 

[Dr.Peterson]

I would guess that Stefanie has recently learned these theorems:

Rules for Chords. Secants, Tangents - MathBitsNotebook(Geo)

mathbitsnotebook.com

These are proved from drawings like yours, and can be used a little more easily for this problem. The tangent is typically assumed, though it should indeed be stated.

 

[pka]

View attachment 27593
View attachment 27592

Suppose that \(O\) is the center of the circle & \(r\) is its radius.
We know that \(OC^2=OD^2+ CD^2\). Then \((r+10)^2=r^2+16^2\)
Solve for \(r\)