# How do I model this boundary problem?

A circle of center (3,0) and radius 3 intersects another circle of center (0,0) and radius "h". Let a =(0,h) and b be the point of intersection of both in the first quadrant, (0 <h≤). If Les the line that passes through A and B, also (z, 0) is the point of intersection of L with the axis of the abscissa. Find the value of "lim h → 0 (z)"

• @Jhon Paye - Por favor traduce al inglés. El español no es el primer idioma en este sitio. – Taylor Rendon Jun 30 at 3:48
• @Jhon Paye: What have you tried? Show your own efforts. – Harish Chandra Rajpoot Jun 30 at 4:05

The point $$b$$ can be found as the point of intersection of $$x^2 + y^2 = h^2$$ and $$(x-3)^2 + y^2 = 9$$
$$x^2 + 9 - (x-3)^2 = h^2$$
$$\implies 3(x+3) = h^2-9$$
$$\implies x = \frac{h^2 - 18}{3}$$
Corresponding $$y$$ can be obtained for point b by substituting in the equation, and then find $$z(h)$$