Question

Find the m of arc AB, round to nearest tenth.

Answer 1

80°

Explanation:

AB and AC are chords.

Chords AB and AC are at a distance of 2 units from the center of the circle.

-> Chord AB = Chord AC

`\implies m(\widehat {AB})=m(\widehat {AC})`...(1)

(Equal chords intercept equal arcs)

`m(\widehat {AB})+m(\widehat {AC})+m(\widehat {BC})=360\degree`

(By arc sum property of a circle)

`\implies m(\widehat {AB})+m(\widehat {AB})+200\degree=360\degree`

(From equation 1)

`\implies 2m(\widehat {AB})=360\degree-200\degree`

`\implies 2m(\widehat {AB})=160\degree`

`\implies m(\widehat {AB})=(160\degree)/(2)`

`\implies \huge{\orange{m(\widehat {AB})={80\degree}}}`