Exercise 9.1

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.

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

So, QR =≠ YZ

Considering the triangles, ∆PQR and ∆XYZ

PQ = (radii are equalnot equal)

PR = (radii are equalnot equal)

QR = (chords are equalnot equal)

By congruency rule, ∆PQR ≅ ∆.

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

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

By the given diagram we need to prove the angles of PQR and XYZ.

In ∆PQR and ∆XYZ we have

PR = (radii are equalnot equal)

PQ = (radii are equalnot equal)

∠PQR = ∠ (given)

∆PQR ≅ ∆ (By congruency rule)

Hence proved, QR = (using CPCT)