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Question

X is a point outside of a circle whose center is O. From X, a tangent whose length is a is drawn to the circle and the shortest distance from X to the circle is a2. Find the radius of the circle.

A
3a4
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B
3a2
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C
12a
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D
a
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Solution

The correct option is B 3a4
The given circle has centre at O, radius OP=OA=r,PX=a is the tangent to the circle at P and AX=a2.(AX is the shortest length )
OPX=90o i.e. ΔOPX is a right triangle , the hypotenuse being OX.
Now AX=a2,OX=OA+AX=r+a2,PX=a and OP=r.
OP2+PX2=OX2
r2+a2=(r+a2)2
ar=3a24=r=3a4

101530_97223_ans_a5f31657a6ba4778b6970faabda83941.png

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