Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 62Square diagonal and Inscribed Circle. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
Let A:(0,0),B:(0,s),C;(s,s) and D:(s,0) with s =side of square. Therefore,O:(s/2,s/2) & Arc BD: x^2+y^2=s^2 and the circle:(x-s/2)^2 + (y-s/2)^2 =s^2/4. E is:[(s(5 -V7)/8,s(V7+5)/8]. Now,CE^2=[(s-(s(5-V7)/8)]^2+[s-s(V7+5)/8)]^2 = s^2/2 or CE =s/V2But BD^2 = 2s^2 or BD = V2s which gives the desired result viz. CE = BD/2Ajit: email@example.com