Geometry
# Properties of Triangles

In a certain right triangle, the hypotenuse equals \((x+z)\) while the other two sides are \((x+y)\) and \((y+z)\) for positive integers \(x, y, z\).

If \(y+4=z\) and \(z>x\) , then compute \(\dfrac{z}{x}\).

\(ABC\) is an isosceles triangle with \(AC = BC\). Furthermore, \(D\) is a point on \(BC\) that bisects the angle at \(A\).

If \(\angle B = 72^\circ\) and \(CD=1,\) then find length of \(BD\) (upto 3 decimal places).

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