The distance of a chord from the centre of a circle of radius 7cm is 5cm,what is the length of the chord to the nearest centimetre?

To find the length of the chord, we can use the Pythagorean theorem.

Let's label the distance from the center of the circle to the chord as "x" and the length of the chord as "c". The radius of the circle is 7 cm.

Using the Pythagorean theorem, we have:
x^2 = (radius)^2 - (distance from center to chord)^2
x^2 = 7^2 - 5^2
x^2 = 49 - 25
x^2 = 24
x = √24
x ≈ 4.9 cm

To find the length of the chord, we need to double x (since the chord spans on both sides of the center):
c = 2x
c = 2 * 4.9
c ≈ 9.8 cm

Therefore, the length of the chord to the nearest centimeter is 10 cm.

To calculate the length of the chord, we will use the following formula:

Length of Chord = 2 * √(r^2 - d^2)

Where:
- r is the radius of the circle
- d is the distance of the chord from the center of the circle.

Given that the radius (r) is 7 cm and the distance of the chord (d) is 5 cm, we can substitute these values into the formula:

Length of Chord = 2 * √(7^2 - 5^2)
Length of Chord = 2 * √(49 - 25)
Length of Chord = 2 * √24
Length of Chord = 2 * √(4 * 6)
Length of Chord = 2 * (2√6)
Length of Chord = 4√6

Since we are asked to round the length of the chord to the nearest centimeter, we can calculate the approximate value using a calculator or estimation technique:

4√6 ≈ 4 * 2.45

Calculating this, we find that the length of the chord is approximately 9.8 cm.

Therefore, the length of the chord, rounded to the nearest centimeter, is 10 cm.

draw a radius perpendicular to the chord.

If the center of the circle is O, the chord is AB, and the midpoint of the chord is P, then you have a right triangle where the leg OP is 5, and the hypotenuse (the radius) is 7. So, PA=PB is half the chord length.