Secants, Tangents, Chords

Multiple Choice

If m∠LNM = 280°, what is the value of y in the circle diagram?

• 40

• 80

• 160

• 140

Open Ended

Why is it important to understand the properties of angles and arcs in circles when solving geometric problems?

Multiple Choice

According to Theorem 10.11, what is the measure of an angle formed by a tangent and a chord intersecting at a point on a circle?

• It is equal to the measure of the intercepted arc

• It is half the measure of the intercepted arc

• It is twice the measure of the intercepted arc

• It is equal to the sum of the intercepted arcs

Multiple Choice

How do you find the measure of an angle formed by two chords intersecting inside a circle, according to Theorem 10.12?

• It is half the sum of the measures of the intercepted arcs

• It is equal to the measure of one intercepted arc

• It is half the difference of the measures of the intercepted arcs

• It is twice the measure of the intercepted arcs

Fill in the Blanks

Fill in the blank: The measure of an angle formed outside the circle by two secants is equal to

the difference of the measures of the intercepted arcs.

Open Ended

Explain the difference between the formulas for angles formed inside the circle and outside the circle by chords, tangents, or secants.

Multiple Select

Which of the following are necessary to find the value of x in the problem where two secants intersect outside the circle?

• The measures of both intercepted arcs

• The measure of the angle formed

• The radius of the circle

• The length of the secants

Fill in the Blanks

Fill in the blank: The measure of angle LM in the circle is

degrees.

Open Ended

Reflecting on today's lesson about circles and their angles, what is one concept you found most interesting or challenging?