Two concentric circles form an annulus

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Quandaries & Queries

In the diagram below, two concentric circles form an annulus. The vertical line is tangent to the inner circle, and forms the diameter of a third circle.

Explain why the areas of the annulus and third circle are the same.

Hi,

I added two red lines to your diagram and labeled three points.

circles

Each of the sides of the triangle PCT is a radius of one of the circles. What is the area of each of the circles? Triangle PCT is a right triangle(Why?). What does Pythagoras' theorem tell you about this triangle?

Penny

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