a chord of 42 cm with the distance of 5 cm from center of the circle find the raduis of the circle?/.
Draw the picture
r^2 = 5^2 + 21^2
To find the radius of the circle, we can use the relationship between the radius, chord length, and distance from the center of the circle.
Let's denote the radius of the circle as 'r', the chord length as 'c', and the distance from the center to the chord as 'd'.
We are given that the chord length is 42 cm (c = 42 cm) and the distance from the center of the circle to the chord is 5 cm (d = 5 cm).
Now, let's use the relationship between the chord length, distance from center, and radius:
c^2 = (2r)^2 - (2d)^2
Substituting the given values:
42^2 = (2r)^2 - (2 * 5)^2
Simplifying further:
1764 = 4r^2 - 100
Rearranging the equation:
4r^2 = 1764 + 100
4r^2 = 1864
Dividing both sides by 4:
r^2 = 1864 / 4
r^2 = 466
Taking the square root of both sides:
r = √466
Therefore, the radius of the circle is approximately 21.59 cm (rounded to two decimal places).