A chord of a circle is 9cm. If its distance from the centre of the circle is 5cm,calculate the radius of the circle
The radius of the circle is 6.7 cm
If a chord of a circle is 10cm long. If the chord is 5cm away from the center calculate for the radius
MATH
To calculate the radius of the circle, we can use the Pythagorean Theorem.
First, draw a diagram of the circle. Label the center of the circle as "O", the chord as "AB" with a length of 9 cm, and the distance from the center of the circle to the chord as "CD" with a length of 5 cm.
Since the line joining the center of the circle to the midpoint of the chord is perpendicular to the chord, we can draw a right triangle with line segments CD, OD, and OC.
By applying the Pythagorean Theorem, we have:
OC^2 = OD^2 + CD^2
Let's substitute the values we know into this equation:
OC^2 = r^2 + 5^2
As we are trying to find the radius of the circle (r), we rearrange the equation:
r^2 = OC^2 - 5^2
Substituting the given value for OC (5 cm), we have:
r^2 = 5^2 - 5^2
r^2 = 25 - 25
r^2 = 0
Taking the square root of both sides, we find:
r = 0
Therefore, the radius of the circle is 0 cm.