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.

Guest Jun 13, 2021

#1**0 **

Idk but how to solve unless the radius is given? Circle LOM is irrelevant to the question.

amygdaleon305 Jun 14, 2021

#2**0 **

Solution:

**If the arc of LM is 72° on the larger circle, then the arc LPM on the larger circle is**

**360 - 72 = 288°**

Am I missing something?

--. .-

Guest Jun 14, 2021

#3**0 **

No that's not right measure of arc is given in degrees or radian but that doesn't mean you can simply subtract it from 360 to calculate the length of larger arc. The formula for length of arc is

length of arc \(= \theta × {\pi r\over 180}\)

where \(\theta\) is the angle subtended by respective arc at the centre and r is the radius.

So, we need the radius to calculate..

amygdaleon305
Jun 15, 2021

#4**+1 **

Hi Amy,

The question only asks for the arc (an angular measure) of LPM, in degrees. It gives the arc of LM as 72 degrees.

All circles have 360 degrees, and all angular measurements of a circle are constant for any radius.

Of course, the __linear__ measure of the arc __length__ is proportional to the radius.

--. .-

GA

Guest Jun 15, 2021

#5**+1 **

Oh okay Ginger I guess I might've overthought it again... thanks for clarifying

amygdaleon305
Jun 15, 2021