Quadrilateral with one side as diameter of circumscribing circle

Problem PG-010
The quadrilateral ABCD shown in Fig. PG-010 is inscribed in a circle with side AD coinciding with the diameter of the circle. if sides AB, BC, and CD are 8 cm, 10 cm, and 12 cm long, respectively, find the radius of the circumscribing circle.
 

Cyclic quadrilateral inscribed in a circle of unknown radius

 

Solution PG-010

 

Another Solution (Using Ptolemy's Theorem)

 

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