(i) Through a point on a circle one tangent lines can be drawn.
Let the centre be O.
From this figure it can be interpreted that OP will be the radius of the circle.
For the line LM which contains the point P, the distance OP<OL because OP is the perpendicular distance and perpendicular distance is always the shortest distance.
OP is perpendicular to LP and MP.
This is possible only when all the L, P and M lie on same line.
Hence LPM is a straight line.
LM is the only tangent which pass through the point P.
Hence only one tangent can be drawn from a point on a circle.
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two Parallel tangents at the most.
A tangent line touches a shape at a single point. Two parallel tangents will be on opposite sides of the circle. If you try to add another parallel line, it will pass through two points of the circle, and isn't a tangent.
(iv) The common point of a tangent to a circle and the circle is called point of contact or point of tangency.
In the above figure P is the point of contact for the tangent LM and Q is the point of contact for the tangent XY.
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