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:

Let QR and YZ be the equal chords of 2 congruent circles.

Then, QR = YZ

We need to prove that they subtend equal angles at the center. That is, ∠QPR = ∠YXZ

We know that the radii of both circles are equal. So, we get: PR = PQ = XZ = XY

Consider the 2 triangles, ∆PQR and ∆XYZ.

PQ = XY (Radii are equal)

PR = XZ (Radii are equal)

QR = YZ (Chords are equal)

By SSS congruency, ∆PQR is congruent to ∆XYZ.

So, by CPCT (Corresponding parts of congruent triangles), we get ∠QPR =∠YXZ.

Hence, proved that equal chords of congruent circles subtend equal angles at their centers.

☛ Check: NCERT Solutions Class 9 Maths Chapter 10

Video Solution:

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

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.2 Question 1

Summary:

If two circles are congruent, they have the same radii, then equal chords of congruent circles subtend equal angles at their centers

☛ Related Questions:

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