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Answer:
radius ≈ 15.5
Step-by-step explanation:
the radius is RS
the angle between a tangent and the radius at the point of contact is 90°
then Δ RST is a right triangle
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
RS² + ST² = RT² ( substitute values )
RS² + 7² = 17²
RS² + 49 = 289 ( subtract 49 from both sides )
RS² = 240 ( take square root of both sides )
RS = ≈ 15.5 ( to 1 dec. place )