1. We are given incomplete statements about angles formed by tangents, secants, and their intersections with circles. We will supply the missing words to make the theorems correct. 2. Statement 1: "If two tangents intersect outside a circle, the measure of the angle formed equals one-half the positive __________ of the intercepted arcs." - The angle formed by two tangents intersecting outside a circle is half the difference of the measures of the intercepted arcs. - Missing word: "difference" 3. Statement 2: "If a secant and a tangent intersect outside a circle, the measure of the angle formed equals __________ the positive difference of the intercepted arcs." - The measure of the angle formed equals half the positive difference of the intercepted arcs. - Missing phrase: "one-half" 4. Statement 3: "If a secant and a tangent intersect on a circle, the measure of the angle formed equals one-half the measure of the __________ arc." - The angle formed equals half the measure of the intercepted arc that touches the point of intersection. - Missing word: "intercepted" 5. Statement 4: "If two secants intersect __________ a circle, the measure of the angle formed equals one-half the positive difference of the intercepted arcs." - Two secants intersecting outside a circle form an angle equal to half the difference of the intercepted arcs. - Missing word: "outside" 6. Statement 5: "If two secants intersect inside a circle, the measure of the angle formed equals one-half the __________ of the measures of the intercepted arcs." - The angle formed inside the circle equals half the sum of the intercepted arcs. - Missing word: "sum" --- Summary of missing words: 1) difference 2) one-half 3) intercepted 4) outside 5) sum --- PROBLEM SOLVING - Activity 4: There is a geometry problem involving a circle and places in Baguio City. Since specific numerical data or questions are not provided, we cannot solve numerical parts here. If you provide specific angle or length values or questions regarding the circle or intersecting lines, I can help solve them step-by-step. slug: "circle theorems" subject: "geometry" desmos: {"latex":"","features":{"intercepts":true,"extrema":true}} q_count: 5