Two chords in a circle are equal in lengh.The distances from the centre of the circle can be represented by x2 and 4x respectively.How far is it chord from the centre of the circle?[Under the topic of properties of a circle.]

if the chords have the same length, they are the same distance from the center. So,

x^2 = 4x
x = 4 or 0

So, they are 16 units from the center.

Or, they are both diameters, passing through the center.

To find out the distance from the center of the circle to the chord, we need to use the properties of a circle.

First, let's assume that the two chords are AB and CD, where AB = CD. Let O be the center of the circle.

According to the circle properties, if two chords in a circle are equal in length, then they are equidistant from the center of the circle.

So, the distances from the center O to the chords AB and CD are equal. Let's represent this distance as y.

Now, we can set up the equations:

From the given information, the distance from the center to the chord AB is x2, and the distance from the center to the chord CD is 4x.

So, we have two equations:

Distance from O to AB = x2
Distance from O to CD = 4x

Since the distances are equal, we can equate these two expressions:

x2 = 4x

To solve this equation, we can rearrange it to the form of a quadratic equation:

x2 - 4x = 0

Factoring out the common term:

x(x - 4) = 0

Setting each factor equal to zero:

x = 0 or x - 4 = 0

If x = 0, it means the distance from O to AB or CD is zero, which is not possible. Therefore, we can discard this solution.

If x - 4 = 0, we can solve for x:

x = 4

Now that we have found the value of x, we can substitute it back into one of the original equations to find the distance from the center to the chord:

Distance from O to AB = x2
Distance from O to AB = 42
Distance from O to AB = 16 (square of 4)

Therefore, the distance from the center of the circle to the chord is 16 units.