1. Problem: Find the equations relating the segments in each circle figure to solve for $x$ using chord and secant-tangent theorems. 2. For each part: a. Two chords intersect inside the circle. The product of the segments of one chord equals the product of the segments of the other: $$ 4 \times x = 3 \times 8 $$ b. A secant and a tangent intersect outside the circle. The product of the whole secant segment and its external part equals the square of the tangent segment: $$ (3 + x) \times x = 9^2 $$ c. A secant and a tangent intersect outside the circle. The product of the whole secant segment and its external part equals the square of the tangent segment: $$ (5 + 15) \times 5 = 8^2 $$ d. Two secants intersect outside the circle. The products of the whole secant and its external part for each secant are equal: $$ (6 + 4) \times 4 = (x + 2) \times 2 $$ e. A secant and a tangent intersect outside the circle. The product of the whole secant segment and its external part equals the square of the tangent segment: $$ (8 + 4) \times 4 = x^2 $$ f. Two chords intersect inside the circle. The product of the segments of one chord equals the product of the segments of the other: $$ 2 \times 20 = 3 \times x $$ These equations can be solved for $x$ accordingly.