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Question

A circle C1 of unit radius touches coordinate axes in first quadrant. Another circle C2 touches C1 externally and also touches each line of pair xy4x4y+16=0. Then radius C2 is

A
423
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B
432
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C
742
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D
642
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Solution

The correct option is D 742
Fromulaused
Distance between two point A(x1,y1)andB(x2,y2)is
AB=(y2y1)2+(x2x1)2
Let the radius of circle C2=r
RadiusofcircleC1=1(given)
xy4x4y+16=0
x(y4)4(y4)=0
(y4)(x4)=0
Hencelinesarex=4,y=4
Nowconsider
The diameter of circle C1andC2 and the lines x=4 and y=4 form a straight line
Hence
OC1+C1C2+C2A=OA
12+12+1+r+r2+r2=42+42
2+1+r+r2=42
1+r+r2=32
r(1+2)=321
r=3211+2
rationalizing
r=3211+2×1212
=742
1929839_1412063_ans_5072a4d388a04633872a44a125aad7d2.JPG

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