Question

The diagram was constructed with straightedge and compass tools. Point A is the center of one circle, and point C is the center of the other. How does the length of segment CE (not shown) compare to the length of segment AD ? Explain your reasoning.

Answer 1

CE = AD/2

Explanation:

C is the center of small circle

• Point E is on same circle, therefore CE = radius of small circle

• AD passes through the center of small circle and both points are on same circle, therefore AD is diameter of small circle

Since diameter is double of radius:

• AD = d, CE= r

• d = 2r

• AD = 2*CE or CE = AD/2