A chord is drawn 3cm away from the centre of a circle of radius 5cm .calculate the length of the chord

Answer 1

To calculate the length of the chord, we can use the Pythagorean theorem.

Let's label the center of the circle as point O, and the endpoints of the chord as points A and B.

Since the chord is drawn 3cm away from the center of the circle, we can draw a perpendicular line from the center to the chord. Let's label the point where this perpendicular line intersects the chord as C.

We can form a right triangle by connecting points O, C, and A.

The length of OA (the radius) is 5cm, and the length of OC (the perpendicular line) is 3cm.

Using the Pythagorean theorem:

AC^2 + OA^2 = OC^2
AC^2 + 5^2 = 3^2
AC^2 + 25 = 9
AC^2 = 9 - 25
AC^2 = -16

Since the length of a line segment cannot be negative, we have made an error in our calculations.

Let's try a different approach.

Instead of connecting points O, C, and A, we can draw a line segment from point O to point B.

This creates a right triangle with length OC as the base and length OB as the hypotenuse.

Using the Pythagorean theorem:

OC^2 + OB^2 = BC^2
3^2 + 5^2 = BC^2
9 + 25 = BC^2
34 = BC^2

Taking the square root of both sides, we find:

sqrt(34) = BC

Therefore, the length of the chord is approximately 5.83 cm.