Question

1. this diagram was constructed with straightedge and compass tools. a is the center of one circle, and c is the center of the other. select all true statements.

ab = bc
ab = bd
ad = 2ac

Explanation:

Step1: Recall circle - radius property

In a circle, all radii are equal. Since \(A\) is the center of one circle and \(AB\) and \(AC\) are radii of the circle with center \(A\), \(AB = AC\). Since \(C\) is the center of the other circle and \(BC\) and \(CD\) are radii of the circle with center \(C\), \(BC=CD\).

Step2: Analyze \(AB = BC\)

There is no information to suggest that the radii of the two - circles are equal. So, \(AB
eq BC\) in general.

Step3: Analyze \(AB = BD\)

There is no geometric relationship from the construction that would imply \(AB = BD\).

Step4: Analyze \(AD = 2AC\)

We know that \(AD=AC + CD\). Since \(CD = AC\) (because \(AB = AC\) and \(BC = CD\) and the way the circles are constructed), then \(AD=AC+AC = 2AC\).

Answer:

AD = 2AC