# Arcs & Angles

- Author:
- karen.handy

- Topic:
- Angles

An angle with its

__is called a__**vertex at the center of a circle****central angle**. An angle__of a circle and__**whose sides are chords**__is called an__**whose vertex is on the circle****inscribed angle**. In this activity you'll investigate relationships among central angles, inscribed angles, and the arcs they intercept.Points B & C divide Circle A into two arcs. The shorter arc is called a minor arc and the larger one is called a major arc. A minor arc is named after its endpoints.
You can drag points B & C to change the measure of the arc. (Because point B was used to construct the circle; moving it will also change the size of the circle.)
1) Construct segment AB & segment AC. Measure BAC
2) Drag point C around the circle and observe the measures. Pay attention to the differences when the arc is a minor arc & when it is a major arc.
CDB.

**Q1**Write a conjecture about the measure of the central angle & the measure of the minor arc it intercepts.**Q2**Write a conjecture about the measure of the central angle and the measure of the major arc it intercepts. 3) Place point D on the circle. Open the Style menu. Change the from dashed to solid line. Construct segment DB & segment DC Measure4) Drag point C and observe the measures of the arc angle & CDB.
CDB.

**Q3**Write a conjecture about the measure of an inscribed angle & the arc it intercepts. 5) Drag point D (without crossing points B or C), and observe the measure of**Q4**Write a conjecture about all inscribed angles and their intercepted arcs. 6) Drag point C so that the measure of the central angle is 180**Q5**Write a conjecture about angles inscribed in a semicircle.