Exploring Tangents and Radii in Circles

The video tutorial explains how to find the length of segment AC, which is tangent to circle O at point C. It begins by establishing that line AC is perpendicular to the radius OC, forming a right triangle AOC. The Pythagorean theorem is then applied to calculate the length of segment AC, given the known lengths of the other sides. The tutorial concludes with the solution that the length of segment AC is 4.

What does it mean when a line is tangent to a circle at a point?

• The line intersects the circle at exactly one point.

• The line intersects the circle at two points.

• The line is parallel to the circle's radius.

• The line is inside the circle.

Why is triangle AOC considered a right triangle?

• Because line AC is tangent to circle O at C.

• Because line AC is parallel to OC.

• Because OC is the longest side of the triangle.

• Because AOC is an equilateral triangle.

What property does a tangent line have in relation to a circle's radius at the point of tangency?

• It is parallel to the radius.

• It intersects the radius at a 45-degree angle.

• It bisects the radius.

• It is perpendicular to the radius.

What is the length of the radius of circle O?

• 3 units

• 2 units

• 5 units

• 4 units

How do we determine the length of segment AC?

• By calculating the area of triangle AOC.

• By applying the Pythagorean theorem.

• By measuring the diameter of circle O.

• By using the circumference of circle O.

What additional information is needed to apply the Pythagorean theorem to triangle AOC?

• The length of segment AB.

• The area of circle O.

• The diameter of circle O.

• The circumference of circle O.

What is the correct formula to calculate the length of AC?

• AC^2 + OC^2 = AO^2

• AC^2 = OC^2 + AO^2

• AC^2 + AO^2 = OC^2

• OC^2 + AO^2 = AC^2

What is the length of the hypotenuse in triangle AOC?

• 2 units

• 4 units

• 3 units

• 5 units

What is the length of segment AC?

• 2 units

• 3 units

• 4 units

• 5 units

After applying the Pythagorean theorem, what equation do we get to find the length of AC?

• AC^2 = 25 - 3

• AC^2 + 9 = 25

• AC^2 = 25 + 9

• AC^2 + 3 = 25