Students can Download Class 9 Maths Chapter 12 Circles Ex 12.2 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 9 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 9 Maths Chapter 12 Circles Ex 12.2

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:

Data : Two circles having centres O and O’ and having equal radius. Chord AB = CD.

To Prove: Equal chords of congruent circles subtend equal angles at their centres.

Or ∠AOB = ∠CO’D

Proof: In ∆AOB and ∆CO’D,

OA = O’C (Data)

OB = O’D (Data)

AB = CD (Data)

∴ ∆AOB ≅ ∆CO’D

∴ ∠AOB = ∠CO’D.

Question 2.

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

Solution:

Circle with centres A and B are congruent and ∠PAQ = ∠RBS

To Prove PQ = RS.

Proof: In ∆APQ and ∆BRS,

AP = BR ……… radii of congruent circles

AQ = BS are equal

∠PAQ = ∠RBS (Data)

∴ ∆PQR ≅ ∆BRS (SAS postulate)

∴ PQ = RS.