Question 1Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

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Let, there be two circles with center P and X with equal radius.

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. NCERT Class 9 Mathematics CBSE Solutions.

From figure,

QR and YZ are equal chords.

In ∆ PQR and ∆ XYZ,

⇒ PQ = XY (Radius of congruent circles)

⇒ PR = XZ (Radius of congruent circles)

⇒ QR = YZ (Chords are equal)

∴ ∆ PQR ≅ ∆ XYZ (By S.S.S. congruence rule)

We know that,

Corresponding parts of congruent triangles are equal.

⇒ ∠QPR = ∠YXZ (By C.P.C.T.)

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

Circles — Question 1

Question 1