Question

.  Study each figure and answer/find what is asked for.

Answer 1

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