Question

Determine the numerical value of x ​

Answer 1

x = 10

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