Question

in a circle chord AB is congruent to chord CD. prove that, arc AC is congruent to Arc BD

Answer 1

Understanding :
1) Length of arc = radius * angle subtended at centre.

For Calculation see pic.

Answer 2

Answer:

Step-by-step explanation:

let a circle with radius r and center O.

in which two chords at equal distance from O are AB and CD.

to prove :- arc AC =ac BD

proof:- in ΔAOB and ΔCOD

AB =CD (given)

OC=OA (radius of circle)

OB=OD (radius of circle)

so ΔAOB ≅ ΔCOD (SSS)

as we know length of arc = radius * angle subtended by arc at center

so arc AC = r* α

and arc BD = r*α

so it is clear that

arc AC =ac BD

hence proved.