A chord is 2cm from the centre of a circle. if the ratius of the circle is 5cm, find the length of the chord
Draw a diagram, including the radii to the ends of the chord. Draw the radius perpendicular to the chord. You now have two right triangles with one leg=1 and hypotenuse=5. Half the length of the chord is √24.
Err, I mean one leg=2. So half the chord has length √21
solve find the radius of a circle .if a chord 24cm long is 5cm distant from the centre
To find the length of a chord, you need to use the formula that relates the radius of a circle to the length of the chord. The formula is:
length of chord = 2 * radius * sin(angle/2)
In this case, the radius of the circle is given as 5cm and the distance from the centre of the circle to the chord is given as 2cm. To find the length of the chord, we first need to find the angle at the centre of the circle that corresponds to the distance from the centre to the chord (which is half the angle formed by the chord).
To find the angle, we can use the relationship between the radius, chord distance, and the angle using trigonometry. In this case, the triangle formed by the radius, chord distance, and the line connecting the centre to the midpoint of the chord is a right triangle.
By using the sine function, we can determine the angle:
sin(angle/2) = chord distance / radius
sin(angle/2) = 2cm / 5cm
sin(angle/2) = 0.4
Now, we can find the length of the chord:
length of chord = 2 * radius * sin(angle/2)
length of chord = 2 * 5cm * 0.4
length of chord = 4cm
Therefore, the length of the chord is 4cm.