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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 $LOM$.

 

 Feb 24, 2024
 #1
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This looks intimidating, but it's completely fine!

\(LO=LM=1\), and \(\angle LOM={90}^{\circ}\), so because it is a right triangle is \(1*1*\frac{1}{2}=\frac{1}{2}\)The area is 1/2.

 Feb 24, 2024

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