Use the image to answer the question.

Question

Two semicircles pass through a horizontal line segment. A vertical line segment connects the two points above and below the horizontal line segment where the semicircles intersect.

Based on the construction marks, what do you know about KO¯¯¯¯¯¯¯¯
and OL¯¯¯¯¯¯¯
?

(1 point)
Responses

KO¯¯¯¯¯¯¯¯=OL¯¯¯¯¯¯¯
Modifying above upper K upper O with bar equals Modifying above upper O upper L with bar

MN¯¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
Modifying above upper M upper N with bar equals Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar

KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯=MN¯¯¯¯¯¯¯¯¯¯
Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar equals Modifying above upper M upper N with bar

MO¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯

Answer 1

Based on the construction marks and the fact that the semicircles intersect the horizontal line segment at points K and L, we can deduce that the segments KO and OL are equal in length.

Therefore, we can conclude that:

\( KO = OL \)

So the correct response would be:

KO¯¯¯¯¯¯¯¯ = OL¯¯¯¯¯¯¯

This assertion is based on the geometric properties of the figure and symmetry, as the line segment connecting the points where the semicircles intersect is vertical and reflects the equivalence of the segments KO and OL.