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Inessa [10]
2 years ago
7

Find the length of the unknown segment (x) in each figure. Use theorem of secant segment and

Mathematics
1 answer:
Over [174]2 years ago
5 0

Answer:

1. x = 6    2. x = 9   3. x = 3

Step-by-step explanation:

Use <u>Intersecting Secants Theorem</u>:

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

1.  AC and AD are secants that intersect at point A

So, AB x AC = AE x AD

         x x 15 = 6 x (6 + 9)

             15x = 90

                 x = 6

2.  KM and KN are secants that intersect at point K

So,  KL x KM = KO x KN

 10 x (10 + 8) = x x 20

              180 = 20x

                  x = 9

3.  IG and IF are secants that intersect at point I

So,  IH x IG = IJ x IF

       x x 39 = 9 x (9 + 4)

           39x = 117

               x = 3

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For this triangle in particular, we can use the special rules of a 30-60-90 triangle

This says:
The opposite side of 30° is: x
The opposite side of 60° is: x * sqrt(3)
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We have our side length for 90° so we just have to work backwards
To find our 30° side length we must divide by 2
8/2 = 4
Which means your y = 4

Now that we have our 30° side length we can just multiple it by sqrt(3)

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Step-by-step explanation:

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