The chord of the circle is perpendicular to the diameter, divides it into parts equal to 24 cm and 6 cm.

The chord of the circle is perpendicular to the diameter, divides it into parts equal to 24 cm and 6 cm. Find the length of this chord.

Find the radius of the circle. To do this, add the length of the segments into which this chord divides the diameter, and divide the result by 2:

R = (24 + 6) / 2 = 30/2 = 15 cm.

If we lower the radius to one of the ends of the chord, then we get a right-angled triangle in which this radius becomes the hypotenuse, and the chord segment and the diameter segment perpendicular to it become the legs. Let’s find the length of the resulting diameter segment:

15 – 6 = 11 cm.

According to the Pythagorean theorem, the chord segment in a given triangle is equal to the square root of the difference between the squares of the hypotenuse and the second leg. Let’s find its length:

√ (15² – 11²) = √ (225 – 121) = √104 ≈ 10.2 cm.

The diameter of the circle divides the chord in half. Therefore, to find its full length, we multiply the result by 2:

10.2 * 2 ≈ 20.4 cm.

Answer: The chord length is approximately 20.4 cm.