Multiple choice

The square of the tangent that can be drawn from any point on one circle to another circle is equal to twice the product of perpendicular distance of the point from the radical axis of two circles and distance between their centres.

  1. True

  2. False
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A Correct answer
Explanation

The power of a point P with respect to a circle is the square of the tangent length. For two circles, the radical axis is the locus of points with equal power. The property stated is a standard theorem in geometry regarding radical axes.

AI explanation

The length of a tangent from a point to a circle equals the square root of the power of the point with respect to that circle. The difference in powers of two circles yields the property that the square of the tangent length equals twice the product of the perpendicular distance to the radical axis and the distance between the circle centres. Thus, the given statement is True.

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