A geometry problem by Aditya Ram
Geometry
Level
3
Two circles of equal radius 'r' are inscribed in a semi-circular sector of radius 1 unit. If they touch each other externally then find 'r'.
The answer is 0.4142.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The distance from the center of the smaller circle to the center of the semicircle is r\sqrt { 2 }. And the radius of the semi circle R is now equal to r+r\sqrt { 2 }. Since R=1, solve for r which is sqrt { 2 }-1