In a circle with a radius of 226cm long, a chord measures 448cm. Determines the length of the two segments into which the chord divides the diameter perpendicular to it

To find the lengths of the two segments into which the chord divides the diameter perpendicular to it, we need to use the Pythagorean theorem. First, let’s find the distance from the center of the circle to the chord (denoted as d). Using the formula for the distance from the center to the chord:

d = \sqrt{r^2 - \left(\frac{c}{2}\right)^2}

where r is the radius and c is the length of the chord. Plugging in the given values:

d = \sqrt{226^2 - \left(\frac{448}{2}\right)^2} = \sqrt{226^2 - 224^2}

d = \sqrt{51076 - 50176} = \sqrt{900} = 30 \, \text{cm}

Now, the full diameter (2 times the radius) will be divided into two segments by the chord. The segments can be determined by the distance from the center to the chord and the radius. Since the diameter is 2 times the radius, the length of each segment is:

r + d = 226 + 30 = 256 \, \text{cm}

r - d = 226 - 30 = 196 \, \text{cm}

Therefore, the lengths of the two segments into which the chord divides the diameter perpendicular to it are 256 cm and 196 cm.