△ABC is an equilateral triangle with side 4 units and a circle inscribed in it. A line segment goes from a vertex C to the midpoint of AB, M. What is the ratio of the length outside the circle to the length inside it of this line segment CM?
The figure given by the question is as below
Midpoint of each side is the point where the side 'touches' the circle, i.e., midpoint of CB, i.e., T is the
point where CB touches the circle.
We are asked to find the ratio CP:PM
By power of a point theorem,
△CMB is a right angled triangle with MB=2, CB=4
Using (1) & (2)
∴ Ratio CP:PM=4√:16√