SOLUTION: Show algebraically that the circles whose equations are x^2+y^2=16 and x^2+y^2-20x+64=0 are externally tangent. Find the area of their point of tangency.

Question 260160: Show algebraically that the circles whose equations are x^2+y^2=16 and
x^2+y^2-20x+64=0 are externally tangent. Find the area of their point of tangency.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Show algebraically that the circles whose equations are x^2+y^2=16 and
x^2+y^2-20x+64=0 are externally tangent. Find the area of their point of tangency.
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x^2+y^2=16
This circle is about the Origin and r = 4
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x^2+y^2-20x+64=0
Complete the square:
x^2-20x+100 + y^2+64=100
(x-10)^2 + y^2 = 36
This circle's center is (10,0) and r = 6
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The 2 radii add to 10, the same as the distance between the centers so they're tangent.
The point of tangency is (4,0). They're tangent, there's no area involved.

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