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Question
The chords corresponding to congruent arcs of a circle are congruent. Prove the theorem by completing following activity.
Given: In a circle with centre B
arc APC ≅ arc DQE
To Prove: Chord AC ≅ chord DE
Proof: In ΔABC and ΔDBE,
side AB ≅ side DB ...`square`
side BC ≅ side `square` ...`square`
∠ABC ≅ ∠DBE ...[Measure of congruent arcs]
∆ABC ≅ ∆DBE ...`square`
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Solution
Given: In a circle with centre B
arc APC ≅ arc DQE
To Prove: Chord AC ≅ chord DE
Proof: In ΔABC and ΔDBE,
side AB ≅ side DB ...\[\boxed{\text{[Radii of the same circle]}}\]
side BC ≅ side \[\boxed{\text{BE}}\] ...\[\boxed{\text{[Radii of the same circle]}}\]
∠ABC ≅ ∠DBE ...[Measure of congruent arcs]
∴ ∆ABC ≅ ∆DBE ...\[\boxed{\text{[SAS test of congruency]}}\]
∴ chord AC ≅ chord DE ...[Corresponding sides of congruent triangles]
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