# CBSE Class 9 - Circles - NCERT Exercise 10.2 + Questions

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.

Given: Circle C (A, r) and C (P, r) are two congruent circles such that BC = QR.

To prove: ∠BAC = ∠QPR

Proof: In ∆ABC and ∆PQR,

BC = QR [ Given]

AB = PQ [ Radii of congruent circles]

AC = PR [ Radii of congruent circles]

Hence, ∆ABC ≅ ∆PQR [SSS Congruency rule]

∴ ∠BAC = ∠QPR [CPCT]

Question 2: Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Given: Two congruent circles with centres O and O'. AB and CD are chords of circles with centre O and O' respectively such that ∠AOB = ∠CO'D

To Prove: AB = CD

Proof: In triangles AOB and CO'D,

AO = CO'

BO = DO' [Radii of congruent circle]

∠AOB = ∠CO'D [Given]

∆AOB ≅ ∆CO'D  [SAS axiom]

AB = CD Proved. [CPCT]

Question 3 (MCQ): Number of circles that can be drawn passing through two points are

(a) one

(b) two

(c) infinite

(d) no circle can be drawn

Question 4 (MCQ): The collection of all points in a plane which are at a fixed distance from a given point of the plane is called

(a) Centre

(b) Circumference

(d) Circle

Question 5 (Fill in the blanks): The fixed point is called the _______ of the circle and the fixed distance is called the  of the circle.

Question 6(MCQ):  The longest chord of a circle is called

(b) Segment

(c) Diameter

(d) Circumference