Question

length of the longest chord of a circle is 18.4 cm, find its radius.

Answer 1

come on -- the longest chord is the diameter.

So, ...

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the radius of a circle given the length of its longest chord, we can use the following formula:

r = √(c^2 - d^2) / 4

Where:
r = radius of the circle
c = length of the chord
d = distance between the midpoint of the chord and the center of the circle

In this case, we are given the length of the longest chord, which means it is also the diameter of the circle. Therefore, the distance between the midpoint of the chord and the center of the circle (d) is half the length of the chord.

d = c/2

Substituting this value into the formula, we have:

r = √(c^2 - (c/2)^2) / 4
r = √(c^2 - c^2/4) / 4
r = √(3c^2/4) / 4
r = (√3/2) * c / 4

Substituting the given value for c:

r = (√3/2) * 18.4 / 4
r ≈ 3.18 cm

Therefore, the radius of the circle is approximately 3.18 cm.

Answer 3

[AI-generated answer — Explain Bot]

To find the radius of a circle given the length of its longest chord, we can use the fact that the perpendicular bisector of a chord passes through the center of the circle.

First, let's draw a diagram to represent the situation. We have a circle with a chord and its center. Label the center as 'O', the midpoint of the chord as 'M', and the endpoints of the chord as 'A' and 'B'.

Next, connect points 'O' and 'M' to form the perpendicular bisector of the chord. This line passes through the center of the circle.

Now, we have formed a right-angled triangle OAM. The longest chord, AB, is the hypotenuse of this triangle, and AM is the radius of the circle.

We can use the Pythagorean theorem to find the length of the radius. The theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:

AM^2 + OM^2 = AO^2

Since AM is the radius, and the perpendicular bisector passes through the center, OM is also equal to the radius, and AO is equal to twice the radius. Therefore, the equation becomes:

(r)^2 + (r)^2 = (2r)^2

Simplifying this equation:

r^2 + r^2 = 4r^2

2r^2 = 4r^2 - r^2

2r^2 = 3r^2

r^2 = 2r^2

Now, let's solve for r:

r^2 = 2r^2

r^2 - 2r^2 = 0

-r^2 = 0

r = 0

However, a circle cannot have a radius of 0, so there must be an error in our calculations.

Let's reassess the problem. We know that the length of the longest chord is 18.4 cm. This corresponds to the diameter of the circle, as any chord passing through the center is a diameter. So, the diameter of the circle is 18.4 cm.

The radius of a circle is half of its diameter, so the radius is:

r = 18.4 cm / 2

r = 9.2 cm

Therefore, the radius of the circle is 9.2 cm.