Question

AC= Help me please!! Thanks so much

Answer 1

Answer:

AC = 6√3 in

Step-by-step 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.

         $\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}$

            Ф = 120°

                Arc length = 4π

            $\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in$

$\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}$

                         $\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}$

$\sf \boxed{\bf AC = 6\sqrt{3} \ in}$