SOLUTION: in each diagram, line ZY is tangent to circles O and P. Find the value of x circle O has a radius 12 circle P has a radius 9 the distance of line ZY is 25

Question 199305This question is from textbook prentice hall mathmatics geometry _practice worksheet 12-1
: in each diagram, line ZY is tangent to circles O and P. Find the value of x
circle O has a radius 12
circle P has a radius 9
the distance of line ZY is 25 This question is from textbook prentice hall mathmatics geometry _practice worksheet 12-1

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
You do not define x, but we presume it is the distance between centers of the circles.
.
a rough sketch helps
.
remember that tan to circles make perpendicular angles to radius at intersection
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if we use the base as line ZY, we see that it is almost a rectangle,
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if we take the rectangle out, we are left with a right triangle, sides 25 , and (12-9=3),
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with hypotenuse "x",,,,,,we use pythagorous to solve
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x^2 = 3^3 + 25^2,,,,, x= 25.18
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