Find the circle touching a line

Question

I have been struggling with this (probably easy to solve) geometry problem for a while. What are the coordinates of the centre and the radius of the circle?

Answer 1

Hint: Draw a line from the point at which the circle is touching the triangle to the center of the circle. Since this line is perpendicular to the tangent, it is paralel to the line from $(0.67,0.01)$ to $(0.69,0.12)$. Can you see some similar triangles?

Answer 2

In the figure, p, q, m, n are known quantities.

⊿ABE ~ ⊿ACD

This means r : p = (q + r) : n

From which r can be found.

E is the point that divides AD internally in the ratio (q + r) : [n – (q + r)]. Hence, the co-ordinates of E can also be found.