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Circle R is shown where points C, H, X, L, M, and W are on the
circle.
Select all of the statements that must be true.
OmZLXC = 90°
W
mZCNH = 90°
mZXNY+mZYLX = 180°
mZMWC +mZMHC = 180°
mZMWC+mZWMH = 180
R
M
H

Circle R is shown where points C H X L M and W are on the circle Select all of the statements that must be true OmZLXC 90 W mZCNH 90 mZXNYmZYLX 180 mZMWC mZMHC class=


Answer :

Answer:

To determine which statements must be true about the given circle R with points C, H, X, L, M, and W on it, we can analyze the properties of circles and angles:

1. **OmZLXC = 90°**: This statement is true because it describes the relationship between the diameter (Om) and the angle formed by the diameter and a chord (LXC).

2. **mZCNH = 90°**: This statement might not necessarily be true. It depends on the positioning of points C, N, and H. If C, N, and H are collinear and C is the midpoint of HN, then this statement is true. Otherwise, it may not be true.

3. **mZXNY + mZYLX = 180°**: This statement is true by the property of opposite angles formed by intersecting chords in a circle.

4. **mZMWC + mZMHC = 180°**: This statement is true because it describes the relationship between the angles formed by two chords intersecting within a circle and their intercepted arcs.

5. **mZMWC + mZWMH = 180°**: This statement is true if and only if W, M, C, and H are concyclic points, meaning they lie on the same circle. If this condition is met, then the sum of the opposite angles formed by intersecting chords is 180°.

Therefore, the statements that must be true are:

- OmZLXC = 90°

- mZXNY + mZYLX = 180°

- mZMWC + mZMHC = 180°

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