Question

in the figure below, c is between a and d, and b is the mid - point of ac. if ad = 15 and bc = 6, find cd.

Explanation:

Step1: Define segment - relationship

Since \(B\) is the mid - point of \(AC\), then \(AB = BC\). Given \(BC = 6\), so \(AB=6\).

Step2: Use the segment - addition postulate

We know that \(AD=AB + BC+CD\). Given \(AD = 15\), \(AB = 6\) and \(BC = 6\). Substitute the values into the equation: \(15=6 + 6+CD\).

Step3: Solve for \(CD\)

Simplify the right - hand side of the equation: \(6 + 6+CD=12 + CD\). Then, solve the equation \(15=12 + CD\) for \(CD\). Subtract 12 from both sides: \(CD=15 - 12\).

Answer:

3