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Question

The centre of the circle, whose radius is 5 and which touches the circle x2+y2-2x-4y-20=0 at 5,5 is


A

10,5

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B

5,8

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C

5,10

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D

8,9

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E

9,8

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Solution

The correct option is E

9,8


Explanation for the correct option:

Finding the center:

Given equation of circle is

x2+y2-2x-4y-20=0x2-2x+1+y2-4y+4-20=5x-12+y-22=25x-12+y-22=52

Therefore, the center of this circle is 1,2.

Now since the radius of each circle is 5, the point at which both circles touch each other divides the line segment joining both centers into exactly half.

Let h,k be the required center of circle.

By midpoint formula,

5,5=1+h2,k+22h,k=9,8

Therefore, the correct answer is option (D).


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