LENGTH OF A CHORD IS 8CM,RADIUS IS 5CM CALCULATE THE DISTANCE OF THE CHORD FROM THE CENTRE OF THE CIRCLE
the radius, half the chord, and the distance form a 3-4-5 triangle
To calculate the distance of the chord from the center of the circle, we can use the Pythagorean theorem.
Let's assume the distance from the center of the circle to the chord is 'd'.
We can create a right-angled triangle by drawing a line from the center of the circle perpendicular to the chord, so that it intersects the chord at its midpoint.
The radius of the circle is 5 cm, so one-half of the chord's length is 4 cm (since the length of the chord is 8 cm).
Now, we have a right-angled triangle with one side as 5 cm (radius of the circle), the hypotenuse as 8 cm (chord length), and we need to find the other side (distance from the center to the chord).
Using the Pythagorean theorem, we can calculate:
d^2 + 4^2 = 5^2
d^2 + 16 = 25
d^2 = 9
Therefore, d = √9
d = 3 cm
Hence, the distance of the chord from the center of the circle is 3 cm.
To calculate the distance of the chord from the center of the circle, we can use the Pythagorean theorem.
The chord divides the circle into two segments, each with a central angle. Let's call the length of half the chord "a" and the distance from the center of the circle to the chord "h."
Using the Pythagorean theorem, we have:
(radius)^2 = (h)^2 + (a)^2
Substituting the given values, we get:
(5 cm)^2 = (h)^2 + (4 cm)^2
25 cm^2 = (h)^2 + 16 cm^2
(h)^2 = 25 cm^2 - 16 cm^2
(h)^2 = 9 cm^2
Taking the square root of both sides, we find:
h = 3 cm
Therefore, the distance of the chord from the center of the circle is 3 cm.