If O is the centre of the circle. Prove that :

< x + < y = < z

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- Feb 28th 2010, 07:11 AMsnigdhacircle problem..
If O is the centre of the circle. Prove that :

< x + < y = < z - Mar 1st 2010, 01:38 AMGrandad
Hello snigdhaI have added the letters A, B and C to your diagram - see the attached.

Then

$\displaystyle \angle QAR = \angle QBR = \tfrac12z$ (angle at centre)Grandad

$\displaystyle \Rightarrow \angle PAC = \angle PBC = 180^o-\tfrac12z$ (angles on a straight line)

$\displaystyle \Rightarrow x + y +(180^o-\tfrac12z)+(180^o-\tfrac12z)=360^o$ (angle sum of quadrilateral ACBP)

$\displaystyle \Rightarrow x + y+360^o-z =360^o$

$\displaystyle \Rightarrow x + y = z$