Pentagon Inscribed in a Circle

Geometry Level 3

In the figure above, the circumcircle of isosceles triangle $ABC$ , with base $\overline{BC}$ , is drawn with center $O$ and has diameters $\overline{AD}$ and $\overline{BE}$ . If $\overline{AB} = \overline{BO}$ and the area of $\triangle{COD} = 9$ , what is the maximum possible area of pentagon $ABDEC$ ?

Note: The figure is not drawn to scale.

The answer is 45.

1 solution

Aidan Poor
Jul 14, 2018

Here is a hint:

Draw radii $\overline{AO}$ and $\overline{OE}$ . Now, angle hunting (do not forget Thales' theorem) and proving triangles congruent will do the rest.

Pentagon Inscribed in a Circle

The answer is 45.

1 solution

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