A and B are two points on a circle with center O, and C lies outside the circle, on ray AB. Given AB = 24, BC = 30, and OA = 16, find OC.

Guest Jan 1, 2021

#1**+1 **

A and B are two points on a circle with center O, and C lies outside the circle, on ray AB. Given AB = 24, BC = 30, and OA = 16, find OC.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = 30 AC = 54 ED = 32 EC = 32 + DC

BC * AC = DC * EC

30 * 54 = DC (DC + 32) DC = 2(√469 - 8) = 27.31281566

OC = OD + DC OC ≈ 43 ^{5}/_{16}

jugoslav Jan 2, 2021