(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

Power of a point theorem (several cases found online, a few here: http://www.cut-the-knot.org/pythagoras/PPower.shtml )

3. The attempt at a solution

I've drawn the figure, and I recognize that in drawing D, it'd have to lay on the edge of a(n) (imaginary) circle about B with a radius of 6, and that based on that, D could only have 2 possible positions inside the original circle. I've also found that the power of point B w.r.t. the original circle is 36, but I don't know how to proceed to find r (either AO or CO, as far as I can tell).

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# Homework Help: Using Power-of-a-Point Theorem in Geometric Proofs

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