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Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$.  The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn.  If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find the area of triangle $LOM$.

 

 Dec 22, 2023
 #1
avatar+129245 
+1

If arc LM  = 90    then angle  LOM  =90  because it is a  central agle in the larger circle

 

Then LOM is a right triangle with legs OM , LM  =1

 

[ LOM ]   =  (1/2) (OM) (LM)   =   (1/2) (1)(1)   = 1/2

 

 

 

cool cool cool

 Dec 22, 2023

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