Point A is on a circle whose center is O, AB is a tangent to the circle, AB = 6, D is inside the circle, OD = 2, DB intersects the circle at C, and BC = DC = 3. Find the radius of the circle.

Question

anonymous · Answer

I'm supposed to be using the "power of a point" theorem to solve this. I only know immediately that the power of B is BA^2 = 36, but I have no way of guaranteeing that D lies on the circle, so I don't know what other power relationships I can make.

anonymous · Answer

If it helps, I know that another value for the power is 36 = BO^2 - r^2...but I've got 2 unknowns there. Unless I can make another relationship?

anonymous · Answer

simple calculus problem someone will draw it for you Once you find the area you set pir^2=area then divide by pi and square root it and there you go you get r

anonymous · Answer

I can only use geometric methods, and I'm told that I'm supposed to use the theorem that I mentioned. :P

anonymous · Answer

is there a diagram? D could be anywhere 2 units away from O?

anonymous · Answer

There's no diagram, and yes, D can be anywhere 2 units from O. However, I think that it could cause for some confusion if I just happen to pick a position of D that is a special case, so in my diagram I put D in a direction opposite that of where A is.