This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the length of the chord, we can use the Pythagorean theorem. The distance from the center to the chord, half the length of the chord, and the radius of the circle form a right-angled triangle. Step 1: Determine the radius of the circle. The diameter is given as 26 cm. The radius is half of the diameter. r = diameter2 = 26 cm2 = 13 cm Step 2: Set up the Pythagorean theorem. Let d be the distance from the center to the chord, r be the radius, and (L)/(2) be half the length of the chord. We have a right-angled triangle where the hypotenuse is the radius (r), one leg is the distance from the center to the chord (d), and the other leg is half the chord length ((L)/(2)). The Pythagorean theorem states: r^2 = d^2 + ((L)/(2))^2 Step 3: Substitute the given values into the equation. Given d = 5 cm and r = 13 cm. (13 cm)^2 = (5 cm)^2 + ((L)/(2))^2 169 cm^2 = 25 cm^2 + ((L)/(2))^2 Step 4: Solve for half the length of the chord ((L)/(2)). ((L)/(2))^2 = 169 cm^2 - 25 cm^2 ((L)/(2))^2 = 144 cm^2 (L)/(2) = sqrt(144 cm)^2 (L)/(2) = 12 cm Step 5: Calculate the full length of the chord (L). The full length of the chord is twice half its length. L = 2 × 12 cm L = 24 cm The length of the chord is 24 cm. That's 2 down. 3 left today — send the next one.