Attachment 20678

the circle has radius 1.

OB=arcOA=

Prove that OP= 1-cos

Deduce that OD =

thanks.

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- Feb 3rd 2011, 11:03 AMBabyMiloGeometry Proof
Attachment 20678

the circle has radius 1.

OB=arcOA=

Prove that OP= 1-cos

Deduce that OD =

thanks. - Feb 3rd 2011, 11:55 AMemakarov
is it known that the circle's center lies on the line OP? Is C the center of the circle? If yes, it's pretty obvious that .

For the second equality, let A' be the projection of A on OB. Use the fact that the triangle BA'A is similar to the triangle BOD. - Feb 3rd 2011, 12:07 PMBabyMilo
yes to your questions, but why cp=cos theta

i cant see it, im stupid :)

and can you explain the 2nd part in more details.

thanks. - Feb 3rd 2011, 12:26 PMemakarov
Because . The fact that follows from the definition of cosine.

Quote:

and can you explain the 2nd part in more details.