A chord of a circle at a distance 11 cm from the center is 6cm long. calculate the length of a chord of this circle, which is at a distance 9cm from the center
To solve this problem, we can use the fact that the distance from the center of a circle to a chord is perpendicular to the chord and bisects it. Let's call the length of the chord at a distance of 9 cm from the center "x".
From the problem, we know that the length of the chord at a distance of 11 cm from the center is 6 cm. This chord is longer than the chord at a distance of 9 cm from the center, which means that the length of the chord at 9 cm from the center is less than 6 cm.
Since the distance from the center to the chord at 9 cm is 9 cm, and the distance from the center to the chord at 11 cm is 11 cm, we can form a right-angled triangle with the radius of the circle as the hypotenuse.
Using the Pythagorean theorem, we can find the radius of the circle:
radius^2 = 11^2 - 6^2
radius^2 = 121 - 36
radius^2 = 85
radius = √85 ≈ 9.22 cm
Now, using the fact that the distance from the center to the chord bisects it, we can apply the segment bisector theorem:
9 × 9 = 11 × x
81 = 11x
x = 81/11
x ≈ 7.36 cm
Therefore, the length of the chord at a distance of 9 cm from the center is approximately 7.36 cm.