Question

This figure shows circle O with chords PM and LN .

mPL=10∘
mLM=14∘
mLN=24∘
PM=15 in.



What is ​ LN ​ ?

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Answer 1

A circle with two minor arcs equal in measure.
So LN=PM

Answer 2

The Length of chord LN will also be 15 inches.

Given,

The angle subtended by the Arc PL at the center of circle is 10 degrees.

The angle subtended by the Arc LM at the center of circle is 14 degrees.

The angle subtended by the Arc LN at the center of circle is 24 degrees.

The length of chord PM is 15 inches.

What are the theorems for chords of a circle?

Now from the attached figure,

The Arc PM makes the angle at the center will be equal to the sum of angles made by Arc PL and Arc LM at the center.

So,

The angle made by Arc PM at the center will be

$(10+14=24)$ degree.

We know that if The angle subtended by the Arc at the center of the circle is equal than the chords which makes the Arc will also be equal.

Since,

$PM=15$

So, LN will also be 15 inches.

Therefore, LN is also 15 inches.

For more details about circle and chord, follow the link:

https://brainly.com/question/15567660