UPSKILL MATH PLUS

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Theory:

In the earlier classes, we have learnt the intersection of two lines. Now, let us analyse what happens if a curve and a line are on a plane.

Let us discuss some situations when a circle and a line intersect.

Situation 1: The line $$AB$$ does not touch the circle.

Here, there is no common point between the straight line $$AB$$ and the circle.

Therefore, the number of points of intersection is zero.

Situation 2: The line $$AB$$ touches the circle at one point.

Here, there is one common point $$P$$ between the straight line $$AB$$ and the circle.

The line $$AB$$ is called the tangent to the circle at $$P$$.

Therefore, the number of points of intersection is one.

Situation 3: The line $$AB$$ touches the circle at two points.

Here, there two common points $$P$$ and $$Q$$ between the straight line $$AB$$ and the circle.

The line $$AB$$ is called the secant of the circle.

Therefore, the number of points of intersection is two.

Important!
The line segment inscribed in a circle is called the chord of the circle.

The chord is a sub-section of a secant.