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Equal Tangents (Posted on 2010-10-03) Difficulty: 3 of 5
C(UV) denotes the circle with diameter UV.

T(P,QR) denotes the tangential distance |PS|,
where point P lies outside C(QR), point S
lies on C(QR), and PS is tangent to C(QR).

Let A, B, C, and D be distinct, collinear
points in that order.

Construct a point E on line AD such that
|EF| = T(E,AB) = T(E,CD) = |EG|





















See The Solution Submitted by Bractals    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Construction | Comment 6 of 11 |
(In reply to Construction by brianjn)

Constructing this with Geometers Sketchpad results in |EF| = |GE|, but angles A'FE and C'GE are each larger than 90 degrees and so those two segments do not lie on a tangent line and the distances are therefore not the tangential distance.
  Posted by Charlie on 2010-10-04 12:05:22

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