# Radius of an arch and Pythagoras theorem

A door of width 6 meter has an arch above it having a height of 2 meter. Find the radius of the arch I analysed the problem to calculate the radius of curvature and I could not establish the relation between radius and height. Please someone help me to solve this using Pythagoras theorem on right angled triangle

-

The radius of the arch is $r=2+h$
If you extend the vertical line into a diameter, then you have $2 \times (2r-2) = 3 \times 3$ by power of a point. –  Hao Ye Jul 9 '14 at 7:39