1. ## more circle questions

in attachments

2. Hello, dgenerationx2!

Here's #19 . . .

19. $AB$ is tangent to the circle and $AC$ is a secant.

. . $AD = 4,\;AC = 9.$ . Find $AB.$
Code:
                B        x
* * * - - - - - - * A
*           *       /
*               *   / 4
*                 * D
/
*               /   *
*             /     *
*           / 5     *
/
*      /          *
*   /           *
*           *
C     * * *
Let $AB = x.$

Theorem:
If a tangent and a secant are drawn to a circle from an external point,
the tangent is the mean proportional between the external segment
of the secant and the entire secant.

Hence: . $\frac{AB}{AD} \:=\:\frac{AC}{AB} \quad\Rightarrow\quad \frac{x}{4} \:=\:\frac{9}{x} \quad\Rightarrow\quad x^2 \:=\:36$

Therefore: . $x \:=\:6$