Posted by Mathslover on Wednesday, May 22, 2013 at 4:54am.
Circle Γ with center O has diameter AB=192. C is a point outside of Γ, such that D is the foot of the perpendicular from C to AB and D lies on the line segment OB. From C, a tangent to Γ is drawn, touching Γ at E, where the foot of the perpendicular from E to AB lies within AD. CD intersects EB at F. If CF=110, what is the length of OC?

geometry help  dgewhg, Wednesday, May 22, 2013 at 11:46am
145

geometry help  SOmebody, Thursday, May 23, 2013 at 11:01pm
wrong answer..

geometry help  Alestair, Thursday, May 23, 2013 at 11:25pm
156

geometry help  rajeev bhatt, Saturday, May 25, 2013 at 10:38am
234

geometry help  ashutosh, Sunday, May 26, 2013 at 4:25am
Make a line segment OE. Since OE=OB, angle OEB = angle OBE. This implies that angle FEC = 90  angle OEB = 90  angle OBE = angle DFB = angle EFC.
Thus angle FEC = angle EFC. Thus EC = CF = 110.
Now in right angle triangle CEO, CE = 110, OE = 96. By Pythagoras's theorem
OC^2 = OE^2 + EC^2 = 110^2 + 96^2 = 21316. This implies OC = 146
the correct ans is 146.....and say Thanks.....
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