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
Welcome back — missed you this week. Step 1: Identify the given information. The radius of the circle is r = 8 cm. The angle subtended by the chord at the center is = 90^. Step 2: Form a triangle with the chord and radii. Consider the triangle formed by the two radii connecting the center to the endpoints of the chord, and the chord itself. Let the center be O and the endpoints of the chord be A and B. Then OA = OB = r = 8 cm. The angle AOB = 90^. This means OAB is a right-angled isosceles triangle, with the chord AB as its hypotenuse. Step 3: Apply the Pythagorean theorem. According to the Pythagorean theorem, for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let the length of the chord be c. c^2 = OA^2 + OB^2 c^2 = r^2 + r^2 c^2 = 2r^2 Step 4: Substitute the value of the radius and solve for c. c^2 = 2(8 cm)^2 c^2 = 2(64 cm^2) c^2 = 128 cm^2 c = sqrt(128 cm)^2 c = sqrt(64 × 2 cm)^2 c = 8sqrt(2) cm The length of the chord is 8sqrt(2) cm. Send me the next one 📸