Circle Basics Central Angles Circles, I Circle Basics Central Angles

Definition - Circle A circle is the collection of all points in a plane equidistant from a given point called the center of the circle.

Definition - Circle A circle is the collection of all points in a plane equidistant from a given point called the center of the circle. ⨀𝐶

Example – Identify the parts of a Circle Name the circle Name a radius of the circle Name a chord of the circle Name a diameter of the circle

Example – Identify the parts of a Circle Name the circle Name a radius of the circle Name a chord of the circle Name a diameter of the circle ⨀𝐾

Example – Identify the parts of a Circle Name the circle Name a radius of the circle Name a chord of the circle Name a diameter of the circle ⨀𝐾

Example – Identify the parts of a Circle Name the circle Name a radius of the circle Name a chord of the circle Name a diameter of the circle ⨀𝐾

Example – Identify the parts of a Circle Name the circle Name a radius of the circle Name a chord of the circle Name a diameter of the circle ⨀𝐾

Radius/Diameter By the definition of a circle, the distance from the center to any point on the circle is always the same. Therefore, all radii are congruent (have the same measurement) A diameter is the sum of 2 radii, thus,

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Compute Radius and Diameter Circle A has diameter 𝐷𝐹 , 𝑃𝐺 . If DF = 10, DA = ? If PA=7, PG=? If AG=12, LA=?

Example 2 The diameter of circle A is 10, circle B 20 and circle C 14. Find XB Find BY

Definition – Circumference The circumference of a circle is the distance around the circle. Essentially, the perimeter of a circle, denoted by C.

Definition – Circumference The circumference of a circle is the distance around the circle. Essentially, the perimeter of a circle, denoted by C. Find C if r = 7. Find C if d = 12.5

Definition – Circumference The circumference of a circle is the distance around the circle. Essentially, the perimeter of a circle, denoted by C. Find C if r = 7. Find C if d = 12.5

CW Angles & Arcs

Definition – Central Angle A central angle has the center of the circle as its vertex, and its sides contain two radii of the circle.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

Example 1 – Central Angles Compute the measurement of angle AOD in circle O.

CW 13, part 2