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mochoa4
05.12.2021 •
Mathematics
Line y=2x+3 is tangent to a circle with center (2,-3). Which of the length of the radius of the circle?
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Ответ:
Step-by-step explanation:
Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:
y+3=-1/2(x-2)
We can simplify this to
y= -1/2x-2
We can then check the point of intersection:
-1/2x-2=2x+3
-5=2.5x
x=-2
we can plug this in to the first equation to get y=2(-2)+3=-1
So the point of intersection of the circle and the tangent line is (-2,-1)
Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.
The radius of the circle is![2\sqrt{5}](/tpl/images/2583/1336/0bea1.png)
Ответ:
x = 10
Step-by-step explanation:
It's given in the question that both the traingles JCD & JKL are similar. So their ratio of corresponding similar sides will be proportional to each other.