The diameter of a circle is 30cm and a chord is 12cm from the centre of a circle. Find the length of the chord
To find the length of the chord, we can use the formula for the length of a chord in a circle:
Length of the chord = 2 * radius * sin(theta/2)
In this case, the diameter of the circle is 30 cm, so the radius is half of that, or 15 cm.
The chord is 12 cm away from the center of the circle. This creates a right triangle, where one side is the radius (15 cm), the other side is half of the chord length (since the chord is symmetrical), and the hypotenuse is the distance from the center of the circle to the chord (12 cm).
Using the Pythagorean theorem, we can find the length of the chord.
15^2 + (chord/2)^2 = 12^2
225 + (chord/2)^2 = 144
(chord/2)^2 = 144 - 225
(chord/2)^2 = -81 (not possible)
The equation has no real solutions, which means that there is no chord 12 cm away from the center of the circle.