Answer:
x = 10
Step-by-step explanation:
OA = OD ( both radii of the circle )
OD = OB + BD = x + 16
OB is at right angles to OB ( line from centre to midpoint of chord is right )
Using Pythagoras' identity in right triangle ABO
OA² = OB² + AB² , that is
(x + 16)² = x² + 24²
x² + 32x + 256 = x² + 576 ( subtract x² from both sides )
32x + 256 = 576 ( subtract 256 from both sides )
32x = 320 ( divide both sides by 32 )
x = 10
