Question

The segments in each figure are tangent to the circle at the points shown.
Find each length.

Answer 1

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Answer:

RS = RT = 2

Explanation:

The two tangents from a point are the same length.

RS = RT

y = y^2/2

y^2/2 -y = 0

y(y/2 -1) = 0 . . . . factor out y

Values of y that make these factors zero are ...

y = 0 . . . . . . . . true if points R, S, T are coincident on the circle

y/2 -1 = 0 ⇒ y = 2

Then the segment lengths are ...

RS = RT = 2