Quadrangle AGFD is cyclic having two opposite angles at A and F equal to a right angle.

(AD+DE)*(DE) = EF*EG = EB

Solve this to find x = DE and from this the solution to the problem.

The value of e is easily determined from the given data and can be used to find a necessary condition which must be satisfied by these data in order to have a solution.

2) The corresponding problem {A, r, b

Following figure illustrates such a construction from {A, r

Points {A,G,H,D} can be constructed from the given data and point E is found drawing the tangent from D to the known circle c.

The following list of non-constructible cases is taken from Fursenko.

1) { a, A, b

2) { a, b

3) { a, b

4) { a, b

5) { a, b

6) { a, b

7) { a, b

8) { a, b

9) { a, b

10) { a, b

11) { a, b

TriaConstructionAarb.html

Problem E2499, American Mathematical Monthly 82(1975) p. 1015.

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