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1. A length of chord 12cm long is 8 cm from the centre of the circle

(a)find the radius of the circle
(b) calculate the length of another chord which is 7 cm from the centre of the circle

Draw a diagram. You will see that

(a) r^2 = 6^2 + 8^2
(b) (x/2)^2 + 7^2 = 10^2

Did you know?

Did you know that the position of a chord in a circle can actually reveal information about the circle itself? In this case, a chord that is 12 cm long and located 8 cm from the center of the circle can help us determine various properties. (a) The radius of the circle can be found by subtracting the distance of the chord from the center from the length of the chord itself. In this case, the radius would be 12 cm - 8 cm, resulting in a radius of 4 cm. (b) Additionally, we can calculate the length of another chord that is 7 cm from the center of the circle. By applying the same principle, we can subtract this distance from the radius to determine the length of the chord. Therefore, the length of the second chord would be 4 cm - 7 cm, resulting in a length of -3 cm. However, it's important to note that in this scenario, a negative length is not physically possible, indicating that no such chord exists for this particular circle.