Question

AC=
Help me please!! Thanks so much

Answer 1

AC = 6√3 in

Explanation:

Finding the length of the chord:

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

∠A = ∠C = 30.

∠A + ∠C + ∠AOC = 180 {angle sum property of traingle}

30 + 30 + ∠AOC = 180°

∠AOC = 180 -60

∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

`\sf \boxed{\bf Arc \ length = (\theta)/(180)\pi r}`

Ф = 120°

Arc length = 4π

`\sf 4\pi =(120)/(180)*\pi *r\\\\ r =(4\pi * 180)/(120*\pi )\\\\ r = 6 \ in`

`\sf \boxed{\bf chord \ length = 2rSin \ (\theta)/(2)}`

`\sf b = 2*6*Sin \ (120)/(2)\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * (√(3))/(2)\\\\ \b = 6√(3)`

`\sf \boxed{\bf AC = 6√(3) \ in}`