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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.

The diagram was constructed with straightedge and compass tools. Point A is the center-example-1

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Answer:

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
User Jonathan March
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