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olga_2 [115]
3 years ago
12

Point O is the center of the circle. What is the value of X? Answer options: 24, 15, 27, 20

Mathematics
1 answer:
Tanya [424]3 years ago
4 0

Answer: FIRST OPTION

Step-by-step explanation:

To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:

(Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)

The total measure of the secant shown is:

18+Diameter

If the radius is 7, then the diameter is:

D=7*2=14

Therefore:

Secant\ line=18+14=32

You also know that:

External\ Secant\ line=18\\Tangent\ line=x

Keeping the above on mind, you can substitute values and solve  for x:

x^{2}=32*18

x=\sqrt{576}\\x=24

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