Question

prove that:• the chords corresponding to congruent arc of circle are congruent​

Answer 1

Answer:

Given: Incongruent circles with centres B and R, arc APC ≅ arc DQE To prove: chord AC ≅ chord DE

Proof: [m(arc APC) = ∠ABC (i)

m(arc DQE) = ∠DRE] (ii) [Definition of measure of minor arc]

arc APC ≅ arc DQE (iii) [Given]

∴ ∠ABC = ∠DRE (iv) [From (i), (ii) and (iii)]

In ∆ABC and ∆DRE, [side AB ≅ side DR [Radii of congruent circles]

side CB ≅ side ER] [From (iv)]

∠ABC ≅ ∠DRE ∴ ∆ABC ≅ ∆DRE [SAS test of congruency]

Hope will be helpful ☺️