A Circular Problem

Three circles are mutually tangent. The radii of one circle is 10 units, the radii of the second is 15 units and the radii of the third circle is unknown. If the centers of these circles are connected by straight lines, the area of the enclosed triangle is 340.74 square units. What is the radii of the third circle?

Österreichische Nationalbibliothek (ÖNB), Codex 5203, Regiomontanus, c. 1458

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