Question

given ( fb ) is the diameter of circle and ( fb perp ac ), determine both ( moverarc{ab} ) and ( overline{dc} ).
answer attempt 2 out of 2
arc ( ab = square^circ )
( dc = square )

Explanation:

Step1: Solve for x using chord segments

Since diameter \(FB \perp AC\), it bisects \(AC\), so \(AD = DC\).
\(3x + 5 = 6x - 7\)
\(5 + 7 = 6x - 3x\)
\(12 = 3x\)
\(x = 4\)

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:

Arc AB = \(44^\circ\)
DC = \(17\)