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To solve for
𝑥
x, considering lines that appear tangent as tangent, we apply the principle that tangents from a common external point to a circle are equal in length. Given the lengths
5
𝑥
+
4
5x+4,
47
47, and
135
135, we equate
5
𝑥
+
4
5x+4 to
47
47 since all tangents are equal. Subtracting 4 from both sides yields
5
𝑥
=
43
5x=43, and dividing both sides by 5 gives
𝑥
=
8.6
x=8.6. Therefore, the value of
𝑥
x is
8.6
8.6
.
1 answer
In order to find the value of 𝑥, we can utilize the principle that tangents drawn from a common external point to a circle are equal in length. By examining the lengths of 5𝑥+4, 47, and 135, we can see that they are all equal since they represent tangents to the same circle. Therefore, we can set up the equation 5𝑥+4 = 47. By subtracting 4 from both sides, we get 5𝑥 = 43. Dividing both sides by 5 gives 𝑥 = 8.6. Therefore, the value of 𝑥 is 8.6.