RS Aggarwal Class-9 Arc Properties of Circle ICSE Maths Solutions

RS Aggarwal Class-9 Arc Properties of Circle ICSE Mathematics Solutions Goyal Brothers Prakashan Chapter-14. therefore We provide step by step Solutions of Exercise / lesson-14 Arc Properties of Circle for ICSE Class-9 RS Aggarwal Mathematics .

Our Solutions contain all type Questions with Exe-14 to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.

Board	ICSE
Publications	Goyal brothers Prakshan
Subject	Maths
Class	9th
Chapter-14	Arc Properties of Circle
Writer	RS Aggrawal
Book Name	Foundation
Topics	Solution of Exe-14, to develop skill and confidence
Academic Session	2021-2022

RS Aggarwal Class-9 Arc Properties of Circle ICSE Mathematics Solutions Goyal Brothers Prakashan Chapter-14

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Notes on Arc Properties

Exercise 14

 

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Notes on Arc Properties

 

1. Two circles are congruent, if and only if they have equal radii.
   
2. Two arcs of a circle are congruent if the angles subtended by them at the centre are equal.
   
3. Two arcs subtend equal angles at the centre, if the arcs are congruent.
   
4. If two arcs of a circle are congruent, their corresponding chords are equal.
   
5. If two chords of a circle are equal, their corresponding arcs are equal.
   
6. The angle in a semi-circle is a right angle.
   
7. The arc of a circle subtending a right angle at any point of the circle in its alternate segment is a semicircle.
   

ANGLE SUBTENDED BY AN ARC OF A CIRCLE

Result : Congruent arcs (or equal arcs) of a circle subtend equal angles at the centre.

Theorem  : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Note : Theorem gives the relationship between the angles subtended by an are at the centre and at a point on the circle.

Terms related to circle

 

• Chord: Any straight line segment that’s both endpoints falls on the boundary of the circle is known as Chord. In Latin, it means ‘bowstring’.
• Diameter: Any straight line segment or Chord which passes through the centre of the Circle and its endpoints connects on the boundary of the Circle is known as the Diameter of Circle. So in a circle Diameter is the longest chord possible in a circle.
• Arc: Any smooth curve joining two points is known as Arc. So in Circle, we can have two possible Arcs, the bigger one is known as Major Arc and the smaller one is known as Minor Arc.
• Circumference: It is the length of the circle if we open and straightened out to make a line segment.

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RS Aggarwal Class-9 Arc Properties of Circle ICSE Mathematics Solutions Goyal Brothers Prakashan Exe-14

Page 181

Question 1:

In the given figure arc Ac and arc BD are two equal arcs of a circle. Prove that chord AB and chord CD are parallel.

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Question 2:

Prove that the angle subtended at the centre of a circle, is bisected by the radius passing through the mid point of the arc.

Question 3:

………………….

……………………

…………………….

Question 10:

In the given figure, ABCDE is a pentagon inscribed in a circle if AB = BC = CD, ………………….. find :

(i)……………

……………..

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