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Answer:
√253
Step-by-step explanation:
Extend the lines to the circumference of the circle as shown in my diagram. If QN:NP = 2:3, then QN = 2/5(10) = 4, and NP = 10 - 4 = 6.
Then we use the intersecting secants theorem to find the length ST: 4(10) = 2(14 + ST)
After some rearranging we get ST = 6 (ignore the 4 in the diagram sorry).
Finally we use the intersecting chords theorem to find the radius, r: (r - 13)(r + 13) = 14(6)
Using difference of 2 squares on the left we get r² -169 = 84
So r = √253
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Rewritten by : Barada
