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Question

The chord of the contact of tangents from a point P to a circle passes through Q (Q lies outside the circle). If a1 and a2 are the lengths of the tangents from P and Q to the circle respectively, then PQ is equal to


A
a21+a22
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B
a21+a22
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C
a1+a2
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D
a1+a22
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Solution

The correct option is A a21+a22
Let P(x1,y1) and Q(x2,y2)
and equation of the circle is  x2+y2=a2
Now the eqaution of the chord of the contact of tangents drawn from the P is 
xx1+yy1=a2
this line also passes through Q
x1x2+y1y2=a2
Now a1=x21+y21a2
a2=x22+y22a2
PQ=(x1x2)2+(y1y2)2=x21+y21+x22+y222(x1x2+y1y2)=a21+a22+2a22a2=a21+a22

Mathematics

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