Question

circle define class 9​

Answer 1

Answer:

Circle is the locus of points equidistant from a given point, the center of the circle. ... A circle is a plane figure contained by one line, which is called circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Step-by-step explanation:

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Answer 2

Answer:

(1) A circle is the collection of those points in a plane that are at a given constant distance from a fixed-point in the plane. The fixed point is called the centre and the given constant distance is called the radius of the circle.

A Circle with centre O and radius r usually denoted by C(O,r). Thus, in set theoretic notations, we write C(O,r)={X:OX=r}

(2) A point P lies inside or on or outside the circle C(O,r) according as OP<r or OP=r or OP>r.

(3) The collection of all points lying inside and on the circle C(O,r) is called a circular disc with centre O and radius r.

The set of all points lying inside and on the circle is called a Circular Disc. It is also known as the circular region.

(4) Circles having the same center and different radii are said to be concentric circles.

When two or more circles have the same center but have different radii, they are called as concentric circles, that is, circles with common center.

(5) A continuous piece of a circle is called an arc of the circle.

For Example: Consider circle C (O, r). Let P1,P2,P3,P4,P5,P6 be point on the circle. Then, the pieces P1,P2,P3,P4,P5,P6,P1,P2 etc. are all arcs of the circle C(O,r).

(6) Prove that If two arcs of circle are congruent, then corresponding chords are equal.

Given: Arc PQ of a Circle C(O,r) and arc RS of another circle C(O′,r) such that PQ≅RS

To Prove: PQ=RS

Construction: Draw Line segment OP, OQ, O′R and O′S.Proof:

Case-I When arc(PQ) and arc(RS) are minor Arcs

In triangle OPQ and O′RS, We have

OP=OQ=O′R=O′S=r [Equal radii of two circles]

∠POQ=∠RO′S arc(PQ)≅arc(RS)⇒m(arc(PQ))≅m(arc(RS))⇒∠POQ=∠RO′S

So by SAS Criterion of congruence, we have

ΔPOQ≅ΔRO′S

⇒PQ=RS

Case-II When arc(PQ) and arc(RS) are major arcs.

If arc(PQ), arc(RS) are major arcs, then arc(QP) and arc(SR) are Minor arcs.

So arc(PQ)≅arc(