Question

in the diagram, the length of segment bc is 23 units. what is the length of segment dc? 13 units 18 units 33 units 46 units

Explanation:

Step1: Find the value of \(x\)

Since \(AB = BC\) (perpendicular bisector theorem), we have \(4x + 1=2x + 7\).
Subtract \(2x\) from both sides: \(4x-2x+1 = 2x-2x + 7\), which gives \(2x+1=7\).
Subtract \(1\) from both sides: \(2x+1 - 1=7 - 1\), so \(2x=6\).
Divide both sides by \(2\): \(x = 3\).

Step2: Calculate the length of \(DC\)

Since \(DC = AD\) (perpendicular bisector theorem) and \(AD=4x + 1\), substitute \(x = 3\) into \(4x + 1\).
\(AD=4\times3+1=12 + 1=13\).

Answer:

13 units