In a straight line

Alicia, Bernardo and Carlos are located in a straight line. Alicia is a meter from Bernardo, David is one meter from both Bernardo and Carlos and Alicia is at the same distance from Carlos as David.

How far is Carlos de Bernardo?

The problem only limits the positions of Alicia, Bernardo and Carlos, therefore David does not have to be located in the same line as his companions.

So we have two possible solutions according to the order in which Alicia, Bernardo and Carlos are available on the line.

In case 1 we have to:

If we define the distances between the different points, we have to:
AB = 1; DB = 1; Dc = 1; AD = ac = x; Bh = y; Dh = h

Ahd x² = (1 + y) ² + h²

DHB 1 = Y² + H²

Ad = ac x = 1 + 2y

Solving y = (-1+5½)/4 = 0.618 m (approx)

In case 2 we have to:

Ahd x² = y² + h²
DHC 1 = (x + y) ² + h²
DHB 1 = (1-y) ² + H²

Solving x = (-1+5½)/2 = 1.618 m (approx)