Question

Triangle def is circumscribed about circle o with de=15 df=12 and ef=13

Find the length of each segment whose endpoints are D and the points of tangency on DE and DF

Answer 1

7

Explanation:

You want the tangent lengths from point D for ∆DEF circumscribing a circle, given DE=15, DF=12, DF=13.

Tangent segments

The lengths of the tangent segments from vertex D are ...

d = (DE +DF -EF)/2 = (15 +12 -13)/2 = 7

The tangent segments with end point D are 7 units long.

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Additional comment

The tangents from each point are the same length, so we have ...

d + e = DE . . . . where d, e, f are the lengths of the tangents from D, E, F

e + f = EF

d + f = DF

Forming the sum shown above, we have ...

DE +DF -EF = (d +e) +(d +f) -(e +f) = 2d

d = (DE +DF -EF)/2 . . . . as above

The other tangents are e = 8, f = 5.