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In the figure below,
bar(BD) and
bar(AC) are diameters of circle
P.
What is the are measure of minor arc
DC^(⏜) in degrees?

In the figure below, $\overline{B D}$ and $\overline{A C}$ are diameters of circle $P$ . $\newline$ What is the are measure of minor arc \overparen{D C} in degrees?

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Reflections of functions

Full solution

Q. In the figure below,

\overline{B D}

and

\overline{A C}

are diameters of circle

P

.

\newline

What is the are measure of minor arc \overparen{D C} in degrees?

Identify Relationship: Identify the relationship between the diameters and the circle. Since $BD$ and $AC$ are diameters of circle $P$ , they intersect at the center of the circle and divide the circle into four equal parts. Each part is a right angle,
Determine Center Angle: Determine the angle at the center corresponding to arc $DC$ . Since $BD$ and $AC$ are perpendicular diameters, angle $BPC$ is a right angle, which is $90$ degrees. Minor arc $DC$ corresponds to this angle,
Calculate Arc Measure: Calculate the arc measure of minor arc $DC$ . The measure of an arc in a circle is equal to the angle at the center that it subtends. Therefore, the measure of minor arc $DC$ is $90$ degrees,

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