In the diagram of circle O, tangent PB is drawn as is secant PAC. We wish to prove the Secant/Tangent Length Theorem, i. e. PA x PC = PB^2. (a) Explain why PAB is similar to ΔPBC (i. e. explain which two angles pairs must be congruent and why).
(b) Set up a proportion involving PA, PB, PC, and based on the similar triangles and rewrite it in product form. Draw the two similar triangles separately and in the same orientation to help.

correct

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guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

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