A chord 6.6m long is 5.6m from the centre of the circle.find the radius of the circle.

Make a sketch.

the line from the centre hits the chord at its midpoint and you have a right-angled triangle.

You can use Pythagoras.

r^2 = 3.3^2 + 5.6^2 = 42.25
r = √42.25 = 6.5

Why did the chord go to see the circle doctor?

Because it was feeling a little "off-center"!

But don't worry, I've got your radius solution right here. In a right-angled triangle with the chord as the hypotenuse and the distance from the center as one of the legs, we can use the Pythagorean theorem. Let's call the radius "r" and the distance from the center "d":

r^2 = (6.6/2)^2 + (5.6)^2

Simplifying it, we get:

r^2 = 3.3^2 + 5.6^2

r^2 = 10.89 + 31.36

r^2 = 42.25

Taking the square root of both sides, we find that:

r ≈ √42.25

r ≈ 6.5

So, the radius of the circle is approximately 6.5 meters.

To find the radius of the circle, we can use the relationship between the radius, the chord length, and the distance from the center of the circle to the chord.

Step 1: Draw a diagram to visualize the problem. Label the chord length as 6.6m and the distance from the center to the chord as 5.6m.

Step 2: In the diagram, draw a line from the center of the circle perpendicular to the chord. This line will bisect the chord into two equal parts.

Step 3: We now have a right triangle with the hypotenuse equal to the radius of the circle, one leg equal to half of the chord length (6.6m/2 = 3.3m), and the other leg equal to the distance from the center of the circle to the chord (5.6m).

Step 4: Use the Pythagorean theorem to find the radius:

radius² = leg1² + leg2²
radius² = (3.3m)² + (5.6m)²
radius² = 10.89m² + 31.36m²
radius² = 42.25m²

Step 5: Take the square root of both sides to find the radius:

radius = √(42.25m²)
radius ≈ 6.5m

Therefore, the radius of the circle is approximately 6.5m.

To find the radius of the circle, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we can consider the chord as the hypotenuse of a right triangle, with one side being the distance from the center of the circle to one end of the chord, and the other side being the distance from the center of the circle to the midpoint of the chord.

Let's denote the radius of the circle as 'r'.

According to the Pythagorean theorem, we have:

(r)^2 = (5.6)^2 + (6.6/2)^2

Simplifying this equation, we get:

(r)^2 = 31.36 + 10.89

(r)^2 = 42.25

Taking the square root of both sides, we find:

r = √42.25

r ≈ 6.5

Therefore, the radius of the circle is approximately 6.5 meters.