A chord distant 2cm from the centre of a circle is 18cm long.calculate the length of a chord of the same circle which is 6cm distant from the centre

To calculate the length of the chord that is 6cm distant from the center of the circle, we can use a mathematical relationship known as the "chord theorem."

The chord theorem states that if two chords in a circle are equidistant from the center, then they are congruent (i.e., they have the same length).

So, in this case, we are given that one chord is 2cm distant from the center and has a length of 18cm. We need to find the length of the chord that is 6cm distant from the center.

To solve this, we will use proportions. Let's call the length of the chord we want to find "x."

According to the chord theorem, the length of the chord that is 2cm distant from the center (18cm) is equal to the length of the chord that is 6cm distant from the center (x).

Setting up the proportion:

18cm / 2cm = x / 6cm

Now, we can cross-multiply and solve for x:

18cm * 6cm = 2cm * x

108cm = 2cm * x

Dividing both sides of the equation by 2:

108cm / 2 = x

54cm = x

Therefore, the length of the chord that is 6cm distant from the center is 54cm.

Did you make your sketch?

For the first chord, after drawing in the radius, I have a right-angled triangle, with sides 2, 9 and r, where r is the radius and the hypotenuse

Use Pythagoras to find r
For the 2nd case, let the chord have length 2x, then we have
x^2 + 6^2 = r^2
but you know r^2 from above, so ......