Please help me on my activity in my math subject about Tangents and Secant segments. Thank you!

Make a design of an arch bridge that would connect two places which are separated by a river, 6 " wide. Indicate on the design the different measurements of the parts of the bridge. Out of the design and the measurements of its parts, formulate problems involving tangent and secant segments, and then solve. Use the rubric provided in rate your work. Criteria: Content (50%) Completeness (20%) Creativity (20%) Neatness (10%) Ilustration: Problem: Solution: 10C. TANGENTSECANT / THEOREM: If a secant segment and tangent segment are drawn to a circle from the \\ same external point, the length of the tangent segment is the geometric mean between the length of the secant segment and the length of the external part of the secant segment. TANGENT-SECANT FORMULA: (tangent)2 = (Whole secant) * (external part) Mann? :5 mam FORMULA: a.2 =b*c Q D Proof: 1. diagram 1. Given 2. Two pts. determine only I line. 2. Draw AD. DB 3. MEDAB = - MDB 3. An inscribed 2= its intercepted are. 4. MCCOR = MDB 4. An & formed by tangent and chord Given: secant & tangent 1I - Prove: AC. BC = (DO): its intercepted are. 5. LCELL 5. Reflexive property 6. ACAD - ACDB 6. AA for Similarity of As 7. 7. Corresponding sides of - As are DC - BC in proportion. 8. AC . BC = ( D(): 8. In a proportion, the product of the means = product of the extremes. EXAMPLE 1: Find the value of x. SOLUTION: From the given illustration and conditions, we let a = x, b = 12 + 4 = 16, and c = 4 By substitution, we have a2 = b * C Tangent-Secant Formula (x)2 = (16) * (4) Substitute the values of a, b, and c x2 = 64 Simplify Vx2 = V64 Take the square root of both sides x =8 Simplify Therefore, the value of x segment is 8 units. EXAMPLE 2: Find the value of x. B SOLUTION: From the given illustration and conditions, we let a = x, b = 12 + 6 = 18, and c = 6 X By substitution, we have . O a2 = b * c Tangent-Secant Formula 6 (x)2 = (18) * (6) Substitute the values of a, b, C 12 and c xz = 108 Simplify x2 = V108 Take the square root of both sides x = 6V3 Simplify Therefore, the value of x segment is 6v3 units. EXAMPLE 3: Find the value of y. SOLUTION: From the given illustration and conditions, we let a = 20, b = y + 30, and c = y By substitution, we have a2 = b * C Tangent-Secant Formula (20)2 = (y + 30) * (y) Substitute the values of a, b, and c 400 = y2 + 30y Simplify y2 + 30y - 400 = 0 Addition Property of Equality (y + 40)(y - 10) = 0 Take the factor then simplify y + 40 = 0 y -10 = 0 y = -40 y = 10 Answer. Since we are talking about distance, then we need to take the positive value. Thus, the value of y segment is 10 units