A geometry problem on bicentric quadrilaterals
Geometry
Level
pending
Given that the circumcircle radius is 7 and the distance d, which is the distance between the centres of the circumcircle and incircle is 1
Find the radius of the incircle in the bicentric-quadrilateral.
The answer is 4.8.
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1 solution
If R is the circumcircle radius, r is the incircle radius and d is the distance between the centres of the circumcircle and incircle.
Fuss's theorem states that: \displaystyle \frac{1}{(R-d)^2} + \frac{1}{(R+d)^2} = \frac{1}{r^2}