Question

Theorem 10.2 : If the angles subtended by the chords of a circle ar the centre
or equal, then the chords are equal


.​

Answer 1

Given: A circle with centre o

Answer 2

                        $\huge{\underline{\mathfrak{Theorem\::\:10.2}}}$

Theorem 10.2 states that If the angles subtended by the chords of a circle are equal, then the chords are equal.

Have a look at the diagram in the attachment.

• Given : ∠AOB = ∠COD.

• To Prove : AB = CD.

• Proof :

                      In Δ AOB & Δ COD,

                 AO = CO ( radius of the circle ) --- Side

              ∠AOB = ∠COD ( already given ) --- Angle

                BO = DO ( radius of the circle ) --- Side

Using Side Angle Side congruence ( SAS ), we can say that Δ AOB ≅ Δ COD

Using CPCT ( Congruent parts of corresponding triangles ), AB = CD.

∴ The chords of the circle are equal.