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# Geometry

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Points L and M lie on a circle centered at O, and the measure of arc LM on this circle is 72 degrees.  The circle passing through points O, L, and M is drawn.  Find the measure of arc LPM on the larger circle, in degrees.

Dec 15, 2021

#1
+13023
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Find the measure of arc LPM.

Hello Guest!

Over an arc of a circle, the peripheral angle = 1/2 central angle.

$${\color{blue} ∠\ LPM}=\frac{1}{2}\cdot ∠\ LOM\\ {\color{blue}∠\ LPM=36^o}=\frac{1}{2}\cdot 72^o$$

The arc of the large circle from L via P to M is equal to 360 ° - 72 °, i.e. 288 °.

What is the meaning of the smaller circle, please?

!

Dec 15, 2021
edited by asinus  Dec 16, 2021
#2
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Arc LPM = 360 - 72

What is the measure of arc LOM?

Dec 16, 2021
#3
+13023
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What is the measure of arc LOM?

$$arc\ LOM=72\ Degrees=\frac{9}{20}\pi$$

asinus  Dec 17, 2021