Question

1. given circle o and circle p, match the part of the circle with the correct term. dragable item category central angle major arc inscribed angle semicircle minor arc ∠woj ∠cri (overarc{w s}) (overarc{cir}) (overarc{rci})

Explanation:

Step1: Recall definitions

• Central Angle: An angle whose vertex is at the center of a circle.
• Major Arc: An arc that is larger than a semicircle.
• Inscribed Angle: An angle whose vertex is on the circle and whose sides contain chords of the circle.
• Semicircle: An arc that measures \(180^{\circ}\).
• Minor Arc: An arc that is smaller than a semicircle.

Step2: Analyze each item

• For \(\angle WOJ\): The vertex \(O\) is the center of the circle. So, by the definition of a central angle, \(\angle WOJ\) is a central angle.
• For \(\overarc{WS}\): It is smaller than a semicircle. By the definition of a minor arc, \(\overarc{WS}\) is a minor arc.
• For \(\angle CRI\): The vertex \(R\) is on the circle and its sides \(RC\) and \(RI\) are chords of the circle. By the definition of an inscribed angle, \(\angle CRI\) is an inscribed angle.
• For \(\overarc{CIR}\): It is larger than a semicircle. By the definition of a major arc, \(\overarc{CIR}\) is a major arc.
• For \(\overarc{RCI}\): It measures \(180^{\circ}\) (since \(R\), \(P\), \(I\) are colinear and \(P\) is the center of the circle). By the definition of a semicircle, \(\overarc{RCI}\) is a semicircle.

Answer:

• \(\angle WOJ\): Central Angle
• \(\overarc{WS}\): Minor Arc
• \(\angle CRI\): Inscribed Angle
• \(\overarc{CIR}\): Major Arc
• \(\overarc{RCI}\): Semicircle