If a circle has chord of length 8cm and its radius is 5cm then find the distance of the chord from the centre.
To find the distance of the chord from the center of the circle, we need to draw a perpendicular segment from the center to the chord and determine its length.
Let's label the center of the circle as point O, and we'll label the end points of the chord as A and B.
Since the perpendicular segment from O to the chord bisects the chord, it creates two congruent right triangles.
To find the length of the perpendicular segment from O to the chord, we can use the Pythagorean theorem.
In one of the right triangles, the radius of the circle is the hypotenuse, the perpendicular segment is one side, and half the length of the chord is the other side.
Using the Pythagorean theorem, we can set up the equation:
(Length of perpendicular segment)^2 + (Half the length of the chord)^2 = (Radius of the circle)^2
(Length of perpendicular segment)^2 + (4 cm)^2 = (5 cm)^2
(Length of perpendicular segment)^2 + 16 cm^2 = 25 cm^2
(Length of perpendicular segment)^2 = 9 cm^2
Taking the square root of both sides, we have:
Length of perpendicular segment = 3 cm
Therefore, the distance of the chord from the centre of the circle is 3 cm.