1. The problem involves solving polynomial functions and understanding geometric relations and theorems related to circles, including chords, arcs, central angles, inscribed angles, secants, tangents, segments, and sectors, as well as applying the distance formula. 2. For polynomial functions, the general form is $$P(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$$ where $a_n \neq 0$. 3. To solve polynomial equations, set $P(x) = 0$ and use factoring, synthetic division, or the quadratic formula for degree 2 polynomials. 4. Important circle theorems: - The measure of a central angle equals the measure of its intercepted arc. - The measure of an inscribed angle is half the measure of its intercepted arc. - Chords equidistant from the center are equal in length. - Tangent segments from a common external point are equal. 5. Secants and tangents theorem: If two secants or a secant and a tangent intersect outside a circle, the products of the lengths of the segments are equal. 6. Distance formula between points $(x_1,y_1)$ and $(x_2,y_2)$ is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$. 7. Example: Solve $x^2 - 5x + 6 = 0$. 8. Factor the polynomial: $$x^2 - 5x + 6 = (x - 2)(x - 3) = 0$$. 9. Set each factor to zero: $$x - 2 = 0 \Rightarrow x = 2$$ and $$x - 3 = 0 \Rightarrow x = 3$$. 10. Solutions are $x=2$ and $x=3$. This approach applies to polynomial problems and geometric relations in circles, using theorems and formulas to solve and understand the problems.