Lesson 6 Big Circle Problems - Brian Hayes | Biblioteka

BIG CIRCLE PROBLEMS

Find all of the arc measures of the circle --> arcs sum to 360
Identify where the vertex of the angle is in relation to the circle
Based on the location of the vertex identify the angle : arc (s) ratio
1. Vertex at the center --> angle = arc
2. Vertex ON the circle*** --> angle = 1/2 arc
3. Vertex INSIDE the circle --> angle = 1/2 (sum of the two arcs)
4. Vertex OUTSIDE the circle --> angle = 1/2 (difference of the two arcs)
Identify arc(s) of the angle and Plug and Chug into the angle arc formulas.
NOTE: You will also use vertical angles, linear pairs (supplementary angles), triangle angle sum, exterior angle theorem and other properties to find some of the angles of the circle.

***There is one instance when the vertex is on the circle where you cannot use 1/2 arc to find angle measure. This is when the angle is formed by a chord and a secant (external part). In this case you will have to use another angle to back into this angle. Ocftenyou can use supplementary angles. triangle angle sum, exterior angle theorem, etc to find the angle.

1

tangent to the circle at C

m

Find:

m

1

In circle O m

; m

.

is a tangent.

is a secant.

Find:

m

1

m

: m

is a tangent;

is a secant

Find:

m

1

m

; m

:m

is a diameter of Circle O

is a tangent;

and

are secants

Find:

m

1

In circle O, m

; m

;

and

are diameters.

and

are secants.

Find:

m

1

In Circle O

is a tangent;

is a secant.

.

m

: m

**Hint The arcs "between" parallel chords are equal/congruent.

Find:

m

1

and

are secants.

is a tangent.

m

; m

Find:

m

1

and

are secants.

is a diameter.

m

: m

Find:

m