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 B3a4 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.