Circle

**Category : **9th Class

In this chapter we will study about a non-rectilinear figure circle about which we have studied many things in previous classes.

It is a locus of a point which moves in a plane in such a way that its distance from a fixed point is always constant.

We know that the fixed point is called centre and the fixed distance is called its radius \[\text{D}=\text{2r},\text{ C}=\text{2pr}\] Where D is diameter, C is circumference of circle r is radius.

** Terms Related to Circle**

**Secant**

When a line intersect a circle at two distinct points is called a secant of the circle.

Here, line m is the secant line for circle C(0, r)

**Tangent**

A line which touches the circle at exactly one point is called a tangent to the circle. The point at which line touches the circle is called point of contact. Q is said to be point of contact of tangent.

**Concentric Circles**

Circles are said to be concentric if and only if they have a same centre and different radius.

**Arc**

A continuous piece of circumference of a circle is called arc.

Here, PQ is arc of C(o, r).

**Concurrent Arc**

Two arc are said to be concurrent if they subtend same angle at the centre.

**Minor and Major Arcs**

If the length of an arc is less then the arc of a semicircle then it is called minor arc and which is greater than the semicircles is called major arc. arc \[\overset\frown{PRQ}\] is minor arc and \[\overset\frown{PSQ}\] is major arc

**Segment**

The region bounded by chord and an arc is called segment. The segment which contains minor arc is called minor segment and which contains major arc is called major segment.

**Congruent Circles**

Two circles are said to be congruent if they have same radii.

**Important Properties**

- Equal chord of a circle subtends equal angle at the centre.
- If two arc of a circle are equal then the corresponding chords are equal.
- The perpendicular from the centre of a circle to a chord bisect the chord.
- The perpendicular bisector of the two chords of a circle intersect at the center.
- Equal chords of a circle are equidistant from the centre.

*play_arrow*Circle*play_arrow*Theorems Related to Tangent of a Circle*play_arrow*Circle

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