Answer:A ) The value of x for the given circle with chords and center is 8.3 B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082 Step-by-step explanation:Given two figures :For Figure first A circle with center y , having two chords FM and NM FM = 5 x MN = 2 x + 25 Now from theorem of circle , Chords equidistant from center of circle are equal in length I.e distance of chord MN from center y and distance of FM from center y are equal So, FM = MN Or, 5 x = 2 x + 25 Or, 5 x - 2 x = 25 Or, 3 x = 25 ∴ x = [tex]\frac{25}{3}[/tex] = 8.33 For figure secondThe length of two adjacent chords of circle is 1.2 cm and 0.5 cmLet the center of circle = OLength of chord AB = 1.2 cmLength of chord BC = 0.5 cmAs both chords are at 90° to each other So The Length of diameter of circle AC = [tex]\sqrt{AB^{2}+BC^{2}}[/tex]Or, The Length of diameter of circle AC = [tex]\sqrt{1.2^{2}+0.5^{2}}[/tex]Or, The Length of diameter of circle AC = [tex]\sqrt{1.44+0.25}}[/tex]Or, The Length of diameter of circle AC = [tex]\sqrt{1.69}[/tex]∴ The Length of diameter of circle AC = 1.3 cmSo, Circumference of circle = [tex]\pi d[/tex]Or, Circumference of circle = 3.14 × 1.3 ∴ Circumference of circle = 4.082 cmHence, A ) The value of x for the given circle with chords and center is 8.3B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082 Answer