Question

given fb is the diameter of circle and fb ⊥ ac, determine both m\\(\overarc{ab}\\) and \\(\overline{dc}\\). 15x - 16, 12x + 2, 3x + 5, 6x - 7

Explanation:

Step1: Solve for x using chord segments

Since diameter $FB \perp AC$, $AD=DC$. Set $3x+5=6x-7$.
$3x+5=6x-7 \implies 12=3x \implies x=4$

Step2: Calculate $m\widehat{AB}$

Substitute $x=4$ into $15x-16$.
$m\widehat{AB}=15(4)-16=60-16=44$

Step3: Calculate $\overline{DC}$

Substitute $x=4$ into $6x-7$.
$\overline{DC}=6(4)-7=24-7=17$

Answer:

$m\widehat{AB}=44^\circ$
$\overline{DC}=17$