# What is a Circle? Proves | CBSE Class 9 Maths Solutions

## What is a Circle? Proves | CBSE Class 9 Maths Solutions

In continuation with previous blog Chapter 11 â€“ Circle, today we will learn circle – proves from class 9 Maths.

What is a circle?

• It is the collection of points or locus of a point which moves in a plane in such a way that a distance from a fixed point is constant.
• The fixed point is called the centre.
• The constant distance from the centre is called the radius.

Above figure is a circle with centre O and radius r (it is denoted by C ( O, r)

PROVES

1 A point P which lies inside or outside the circle can be OP< r, OP> r or OP=r

2 Circular Disc

A collection of all points lying inside or on the circle is called the circular disc or circular region.

3 Concentric circles

Circles having the same centre with different radii.

In the above figure, there are two circles having same center O with different radii r1 and r2.

4 Arc

It refers to the continues piece of a circle.

In the above figure P1, P2, P3, P4, P5, and P6 are all arcs on the circle.

5 Corresponding chords are equal if two arcs of a circle are congruent.

PROVE- PQ=RS

Given â€“ Arc PQ of circle 1 and arc RS of the second circle are such that PQRS

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

Given:Â Arc PQ of a CircleÂ C(O,r)Â and arc RS of another circleÂ C(Oâ€²,r)Â such thatÂ PQâ‰…RS
To Prove:Â PQ=RS

There are two cases in the given figure.

Case â€“I Minor Arcs are given- PQ and RS

Given two circles and two triangles

OP=OQ=Oâ€™R=Oâ€™S=r ( raddi of two circles are equal)

POQ=ROâ€™S,

HENCE Î”POQâ‰…Î”ROâ€²S & PQ=RS ( SAS) RULE

Case -2 Major arcs are given PQ and RS

QP and SR are minor arcs so arc PQ â‰… arc RS

So, arc QP â‰… arc SR

QP=SR and PQ=RS

Hence,Â PQâ‰…RSÂ â‡’PQ=RS

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