Understanding Angles Outside a Circle

This video tutorial explores angles formed outside a circle, focusing on three cases: two tangent lines, a tangent and a secant line, and two secant lines. In each scenario, the angle is determined by the difference between the larger and smaller arcs divided by two. Additionally, for the two tangents case, the angle plus the smaller arc equals 180 degrees, and the arcs sum to 360 degrees. These relationships are consistent across all cases, providing a unified approach to solving such geometric problems.

What are the three cases of angles outside a circle discussed in the video?

• Two tangents, tangent-secant, and two secants

• Tangent-secant, two secants, and one tangent

• Two tangents, two secants, and one tangent

• Two tangents, one secant, and one tangent

In the two tangents case, how many points does each tangent line intersect the circle?

• No points

• Three points

• One point

• Two points

In the tangent-secant case, how many times does the secant line intersect the circle?

• Once

• Twice

• Three times

• Four times

In the two secants case, how many times does each secant line intersect the circle?

• Once

• Twice

• Four times

• Three times

Tags

CCSS.HSG.C.A.2

What is the general relationship between the larger arc (B), the smaller arc (A), and the angle outside the circle?

• (B / A) / 2 = angle

• (B + A) / 2 = angle

• (B - A) / 2 = angle

• (B * A) / 2 = angle

Tags

CCSS.HSG.C.A.2

If the larger arc is 90 degrees and the smaller arc is 20 degrees, what is the measure of the angle outside the circle?

• 35 degrees

• 45 degrees

• 30 degrees

• 25 degrees

Tags

CCSS.HSG.C.A.2

In the two tangents case, what is the sum of the angle and the smaller arc?

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

Tags

CCSS.HSG.C.A.2

If the smaller arc is 170 degrees in the two tangents case, what is the measure of the angle?

• 10 degrees

• 20 degrees

• 40 degrees

• 30 degrees

Tags

CCSS.HSG.C.B.5

In the two tangents case, what is the total sum of the larger arc and the smaller arc?

• 450 degrees

• 180 degrees

• 270 degrees

• 360 degrees

Tags

CCSS.HSG.C.A.2

If the larger arc is 190 degrees and the smaller arc is 170 degrees, what is the measure of the angle outside the circle?

• 20 degrees

• 10 degrees

• 30 degrees

• 40 degrees

Tags

CCSS.HSG.C.A.2