The center of a circle having radius 1 is denoted by O. The triangle ABC is inscribed within the circle such that the respective areas of the circular segments described by the sides AB, BC and AC are in the ratio 3:4:5.
A circle with its center located at P is inscribed within the triangle.
Determine the distance OP.
Daniel:
Using an iterative method ( theta(area1)+theta(area2)+theta(area3) = 2pi), I have now obtained:
area(medium) approx. 0.620418 (and less than 0.62041801)
This gives:
theta (small) = 1.8824525260936
theta (med) = 2.10268483077685
theta (big) = 2.2980473161196
Then using theta = 2 arcsin(c/[2r])
Chord(small) 1.61656145662681292
Chord(med) 1.73618078168484268
Chord(big) 1.8247293637203118
Then abc/2(a+b+c) = 0.494581541698617
Using d^2 = R(R2r)
d = 0.10410051201971
I note with simply enormous relief that your findings are not that different!
Edited on September 20, 2010, 3:45 am

Posted by broll
on 20100920 03:40:33 