Answer :

__A Tangent is a line that intersects a circle at exactly one point.__

The tangents drawn at the end points of a chord of a circle can be parallel only if that chord is the diameter of the circle. This will be clear from the fig.1 and fig.2 shown below.

Thus, statement (a) is incorrect.

__A secant is a segment that intersects a circle twice.__

From a point P in the exterior of a circle, infinite no. of secants can be drown through P to the circle. This can be shown in the fig.3 drawn below.

Thus, statement (b) is incorrect.

__A Tangent is a line that intersects a circle at exactly one point.__

From a point P in the plane of a circle, two tangents can be drawn to the circle only if point P is exterior to the circle. This can be shown in the fig.4 drawn below.

Thus, statement (c) is incorrect.

In the above fig.5, we take a point Q on the tangent XY to the circle with centre O. Obviously, this point Q should lie outside to the circle otherwise XY will become secant. And, P is the point of contact. Clearly,

OQ > OP

Also, this is also true for all the points lying on the tangent XY except point P. And,

__we know that perpendicular distance is always the shortest distance__.

OP is shortest of all the distances b/w points O and any other points on XY i.e.

OP ⊥ XY

Hence, The perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Thus, statement (d) is correct.

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