NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 11 |

Chapter Name |
Circles |

Exercise |
Ex 11.2 |

Number of Questions Solved |
2 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.2

**Question 1.**

**Recall that two circles are congruent, if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres**

**Solution:**

Given MN and PQ are two equal chords of two congruent circles with centre at O and O’.

To prove ∠ MON = ∠ PO’Q

Proof In ∆ MON and ∆ PO’Q, we have

MO = PO’ (Radii of congruent circles)

NO = QO’ (Radii of congruent circles)

and MN = PQ (Given)

∴ By SSS criterion, we get

∆ MON = ∆ PO’Q

Hence, ∠ MON = ∠ PO’Q (By CPCT)

**Question 2.**

**Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.**

**Solution:**

Given MN and PQ are two chords of congruent circles such that angles subtended by .

these chords at the centres O and O’ of the circles are equal.

To prove MN = PQ

Proof In ∆ MON and ∆ PO’Q, we get

MO = PO’ (Radii of congruent circles)

NO = QO’ (Radii of congruent circles)

and ∠MON = ∠PO’Q (Given)

∴ By SAS criteria, we get

∆ MON = ∆ PO’Q

Hence, MN = PQ (By CPCT)

We hope the NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.2, help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 11 Circles Ex 11.2, drop a comment below and we will get back to you at the earliest.