THE TRISFXTION OK AN ANGLE. 



Let the diameter BCD (produced) meet the secant AOP in P, 

 making AP equal to the radius. 

 To prove <P=r^<OCB. 



Draw AC. 

 <P=^JArc AB— f\rc OD 



=^(Arc AB+Arc AO) — |(Arc OD + Arc A O) 

 =^Arc OB— J Arc AD=^<OCB— |<P. 

 .•.<P=J<OCB. 



Cor. <COP=f<OCB, since <C0P^<CAE=2<P. 

 Case III. When AOP is a chord (See fig. III). 



Let the diameter BCD meet the chord AO in P, making AP equal 

 to the radius. 



To prove <APC = ^ Reflex <OCB. 

 Draw AC. 



iArc AB. 

 :i Arc OD + ^^A^rc A D + l Arc A B— ^ Arc AD. 



<APCr=^Arc OD- 



=1 Arc OAB 



1 Arc AD. 



