# From San Gaku to Special Relationship?

Geometry Level 3

In the large circle centered at $$O,$$

• both $$\overline{AB}$$ and $$\overline{CD}$$ are its diameters passing through $$O;$$
• the small, orange circle is tangent to $$\overline{AB}$$ at $$P,$$ $$\overline{CD}$$ at $$Q,$$ and circle $$O$$ at $$R;$$
• $$\overline{RQ}$$ and $$\overline{RP}$$ are extended to meet circle $$O$$ at $$X$$ and $$Y,$$ respectively.

True or False?

For any radius of circle $$O$$ and the diameters configuration, $$|AC| = |XY|.$$

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