### Geometry Problems #### Problem 23: **Question**: Find the measure of \(\overset{\frown}{DBC}\) in \(\bigodot P\). **Diagram Explanation**: - A circle is shown with center \( P \) - Points \( A \), \( B \), \( C \), and \( D \) lie on the circumference of the circle. - Angle \( \angle APB \) is given as \( 58^\circ \). #### Problem 24: **Question**: If \(\overline{QT}\) and \(\overline{RW}\) are diameters in \(\bigodot P\), find \( m \overset{\frown}{QW} \). **Diagram Explanation**: - A circle is shown with center \( P \) - Two diameters, \(\overline{QT}\) and \(\overline{RW}\), intersect at the center point \( P \). - Angle \( \angle SQT \) is marked as \( 100^\circ \). - Adjacent angle \( \angle PQW \) is marked as \( 40^\circ \). #### Problem 25: **Question**: Given circle \( O \) with radius 5 and \( OC = 3 \). Find the length of the... (Omitted portion of the problem due to cutoff in the image). ### Detailed Solution Approaches: **For Problem 23**: - To find the measure of \( \overset{\frown}{DBC} \) in circle \( P \), consider the given angle \( 58^\circ \). Use the properties of circle angles and arcs to deduce the measure based on circle theorems. **For Problem 24**: - With diameters \( \overline{QT} \) and \( \overline{RW} \) intersecting at the center, use the geometric properties of diameters and corresponding arc measurements to find \( m \overset{\frown}{QW} \). **Missing Information for Problem 25**: - The problem statement appears incomplete due to the cutoff of the image. To solve, consider the given radius of circle \( O \) and the distance \( OC = 3 \). Employ the Pythagorean theorem or other circle properties to find the missing length. (Note: Full understanding and solving of the problems would typically require application of specific circle theorems