Answer:
8√23 ≈ 38.37
Explanation:
You want the length of a chord 10 units from the center of a circle when a chord 12 units from the center has length 36 units.
Radius
The radius OA completes the right triangle OBA. The hypotenuse (OA) is found using the Pythagorean theorem:
OA² = OB² +BA²
OA² = 12² +18² = 468
Chord
Radius OF is the same length, so we can use the Pythagorean theorem to find FE.
OF² = OE² +FE²
FE² = OF² -OE² = 468 -10² = 368
FD = 2·FE = 2√368 = 8√23
FD ≈ 38.37