Given <BAC =100, <CAT = 20 and <ATC = 40
Also, <CBA = <ATC = 40, since angles in the same segment of a circle are equal
In triangle BAC,
<BCA + <CBA + <BAC = 180
or <BCA + 40 + 100 = 180
or <BCA = 40
Since, <BCA = 40 = <CBA => triangle ABC is an isosceles triangle.
Therefore, AB = AC.
So, arc(AB) = arc(AC) , since equal chords subtend equal arcs
Therefore, arc(AB):arc(AC) = 1:1