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

Circle - Proves | CBSE Class 9 Maths Solutions

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

In continuation with previous blog Chapter 11 – 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.

Circle - Proves | CBSE Class 9 Maths Solutions

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

Circle - Proves | CBSE Class 9 Maths Solutions

2 Circular Disc

 

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

Circle - Proves | CBSE Class 9 Maths Solutions

3 Concentric circles

 

Circles having the same centre with different radii.

Circle - Proves | CBSE Class 9 Maths Solutions

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.

Circle - Proves | CBSE Class 9 Maths Solutions

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 – 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,  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
Circle - Proves | CBSE Class 9 Maths Solutions

There are two cases in the given figure.

Case –I Minor Arcs are given- PQ and RS

Given two circles and two triangles

OP=OQ=O’R=O’S=r ( raddi of two circles are equal)

POQ=RO’S,

HENCE ΔPOQ≅ΔRO′S & PQ=RS ( SAS) RULE

Case -2 Major arcs are given PQ and RS

QP and SR are minor arcs so arc PQ ≅ arc RS

So, arc QP ≅ arc SR

QP=SR and PQ=RS

Hence, PQ≅RS ⇒PQ=RS

Check out other notes form Online Class 9 

 

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