Find the length of a circle? Chord length 3m Height from the middle of the chord to a circumference of 80cm.

AB = 3 m by condition, point K divides AB into 2 equal segments AK = KB = AB / 2 = 3/2 = 1.5 m = 150 cm.
KН = 80 cm – perpendicular to AB.
1. Consider a triangle AKO: angle AKO = 90 degrees, AK = 150 cm and OK – legs, AO – hypotenuse (as well as the radius of the circle).
By the Pythagorean theorem:
AO ^ 2 = OK ^ 2 + AK ^ 2.
2. The segment OH is the radius of the circle, therefore OH = AO. OH consists of two segments OK and KN, where:
OH = AO = OK + KН.
3. Let’s equate two expressions (AO ^ 2 = OK ^ 2 + AK ^ 2 and AO = OK + KN):
OK ^ 2 + AK ^ 2 = (OK + KН) ^ 2.
Substitute the known values:
OK ^ 2 + 150 ^ 2 = (OK + 80) ^ 2;
OK ^ 2 + 22500 = OK ^ 2 + 160OK + 6400;
160OK = 22500 – 6400;
160OK = 16100;
OK = 16100/160;
OK = 100.625 cm.
4. Find the length of the radius:
AO = OH = R = OK + KН;
R = 100.625 + 80 = 180.625 (cm).
5. The circumference is calculated by the formula:
C = 2πR;
C = 2π * 180.625 = 361.25π (cm).
Answer: C = 361.25π cm.