Question

Find the length of the horizontal diameter shown in blue. Show your work.

Answer 1

Diameter =16

Explanation:

Chord theorem: When two chord intersect inside the circle, the product of the products of their segment are equal.

4c * 6 = (2c +8)*4

24c = 2c*4 + 8*4

24c = 8c + 32

Subtract 8c from both sides,

24c - 8c = 32

16c = 32

Divide both sides by 16,

c = 32 ÷ 16

`\boxed{c = 2}`

To find the horizontal diameter, add 2c +8 and 4.

2c + 8 + 4 = 2c + 12

= 2*2 + 12

= 4 + 12

= 16

Diameter = 16