# 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

– : Select Topics : –

**Notes on Arc Properties**

- Two circles are congruent, if and only if they have equal radii.

- Two arcs of a circle are congruent if the angles subtended by them at the centre are equal.

- Two arcs subtend equal angles at the centre, if the arcs are congruent.

- If two arcs of a circle are congruent, their corresponding chords are equal.

- If two chords of a circle are equal, their corresponding arcs are equal.

- The angle in a semi-circle is a right angle.

- 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.

**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.

………….

#### 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)……………

……………..

–: End of **RS Aggarwal Class-9 Arc Properties** of Circle Solutions :–

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