Advertisement Remove all ads

Prove that If Chords of Congruent Circles Subtend Equal Angles at Their Centres, Then the Chords Are Equal. - Mathematics

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

Advertisement Remove all ads

Solution

Let us consider two congruent circles (circles of same radius) with centres as O and O'.

In ΔAOB and ΔCO'D,

∠AOB = ∠CO'D (Given)

OA = O'C (Radii of congruent circles)

OB = O'D (Radii of congruent circles)

∴ ΔAOB ≅ ΔCO'D (SAS congruence rule)

⇒ AB = CD (By CPCT)

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

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

NCERT Class 9 Mathematics Textbook
Chapter 10 Circles
Exercise 10.2 | Q 2 | Page 173
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×