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In circle P, what is the measure of arc CD? Line AC is a diameter and angle APB is a right angle.

A. 218°
B. 52°
C. 62°
D. 180°

User Pebbles
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1 Answer

4 votes

Final answer:

In circle P, the measure of arc CD is 180°, as AC is a diameter that bisects the circle into two semicircles, each measuring 180°.

Step-by-step explanation:

The question involves finding the measure of arc CD in a circle where AC is a diameter and angle APB is a right angle. Since AC is the diameter, it implies that arc CD spans the semi-circle opposite to arc AB. We know that in a circle, the sum of the measures of arcs forming a complete circle is 360°. Therefore, if one semicircle is represented as a straight line as an approximation, its measure would be 180°, which is half of 360°. Consequently, the measure of the semicircular arc CD is 180°.

Since angle APB is a right angle, and it subtends arc AB, arc AB also measures 180° as a semicircle. Therefore, adding the measure of arc AB to the measure of arc CD would result in the full 360° of the circle. Hence, the correct measure of arc CD is option D, which is 180°.

User Lanwen
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