A chord of length 14cm is midway the radius of the circle .calc. the radius of the cicle.
I think you mean that the chord intersects the radius at its middle.
So, draw the figure. You will see that you have a right triangle such that
(r/2)^2 + 7^2 = r^2
Now just solve for r.
Or, recognize that you have a 30-60-90 right triangle, and you know the longer leg.
If 14 cm is midway of the radius, then the radius is 2 times that value.
Why did the chord of the circle go to therapy? Because it was feeling a bit off-center!
But let's get serious, shall we? In a circle, the radius bisects the chord if and only if it is perpendicular to the chord. This means that the chord creates a right angle triangle with the radius, where the chord is the hypotenuse and the radius is the altitude.
Using the Pythagorean theorem, we can find the length of the radius (r) using the length of the chord (c). So, here's the calculation:
Let r be the radius and c be the length of the chord.
Using the midpoint theorem, we know that the line connecting the center of the circle to the midpoint of the chord is perpendicular to the chord and bisects it into two equal halves.
Since the chord is the hypotenuse and the radius is the altitude, we can use the Pythagorean theorem:
r^2 = (c/2)^2 + (c/2)^2
r^2 = (c^2/4) + (c^2/4)
r^2 = (2c^2)/4
r^2 = c^2/2
Now, let's substitute the given value of the chord length (c = 14 cm) into the equation:
r^2 = (14^2)/2
r^2 = 196/2
r^2 = 98
Taking the square root of both sides gives the radius:
r = √98
r ≈ 9.90 cm
So, the radius of the circle is approximately 9.90 cm.
To find the radius of the circle, we can use the formula for the length of a chord in terms of the radius.
The formula is given by:
c^2 = 2r^2 - 2r^2cosθ, where c is the length of the chord, r is the radius of the circle, and θ is the angle subtended by the chord at the center of the circle.
In this case, we know that the length of the chord is 14 cm, and it is midway the radius. This means that the angle subtended by the chord at the center of the circle is 90 degrees.
Substituting these values into the formula:
14^2 = 2r^2 - 2r^2cos90
Simplifying:
196 = 2r^2 - 2r^2(0)
Thus, we have:
196 = 2r^2
Dividing both sides by 2:
98 = r^2
Taking the square root of both sides:
r = √98
Simplifying further:
r = √(49 * 2)
Splitting the square root:
r = 7√2
Therefore, the radius of the circle is 7√2 cm.
To find the radius of the circle, we can use the formula for the relationship between the chord length (c) and the radius (r) of a circle:
r = sqrt((c^2) / 4 + h^2)
Where 'c' is the length of the chord and 'h' is the distance between the midpoint of the chord and the center of the circle.
In this case, we are given that the chord length is 14 cm and it is midway the radius of the circle. Since the chord is midway the radius, it divides the radius into two equal parts.
Let's consider half the chord length, which is 7 cm. This represents the distance between the midpoint of the chord and the center of the circle.
Now we can substitute the values into the formula:
r = sqrt((7^2) / 4 + 7^2)
= sqrt(49 / 4 + 49)
= sqrt(49/4 + (4*49)/4)
= sqrt(49/4 + 196/4)
= sqrt(245/4)
= sqrt(245) / 2
So, the radius of the circle is sqrt(245) / 2, which is approximately 7.88 cm.