The radius of a circle is 12cm
A chord of the circle is 16cm long calculate the distance of the chord form the centre of the circle.Give your answer to 1 decimal place
To solve this problem, we need to use the theorem that states that the perpendicular bisector of a chord passes through the centre of the circle. Drawing a diagram will help us visualize the problem.
Let O be the centre of the circle, and let AB be the chord of length 16cm. We want to find the distance of the chord from O.
Draw a line perpendicular to AB at its midpoint C. This line passes through O, and divides AB into two equal parts of length 8cm.
Let x be the distance from O to C. We can use Pythagoras' theorem to find x:
x^2 + AC^2 = OA^2
OA is the radius of the circle, which is 12cm. AC is half the length of the chord, which is 8cm. Substituting these values, we get:
x^2 + 8^2 = 12^2
x^2 + 64 = 144
x^2 = 80
x = sqrt(80) ≈ 8.9
Therefore, the distance of the chord from the centre of the circle is approximately 8.9cm to 1 decimal place.