Answer to Question #139309 in Geometry for carolyn

Question

Michael has found a circular plate partially buried in the sand. Because Michael doesn't know the size

of the plate, he wants to first find the center of it, and then he will decide whether it is worth it to continue digging. How can Michael find the center of the circle? Show your construction and use mathematics to justify your response with words, symbols, or both.

Answer 1

In our solution we use Thales's theorem:

Michael can find the center of the circle by next method:

The triangles ABC and DAC are similar, and

BC=a, AB=b, DC=2R then:

$\frac{DC}{AC}=\frac{AC}{BC}$ ;

$\frac{2R}{\sqrt{a^2+b^2}}=\frac{\sqrt{a^2+b^2}}{a}$ ;

$R=\frac{a^2+b^2}{2a}$ .

Answer: Michael can find the center of the circle by finding it's radius using two rulers connected in the form of letter T.