Right Triangle and Circle Concepts

This video tutorial covers tangent theorems in geometry, explaining how a line tangent to a circle is perpendicular to the radius at the point of tangency. It includes multiple examples using the Pythagorean theorem to solve for unknowns in right triangles formed by tangents and radii. The tutorial also demonstrates how to simplify square roots and solve complex problems involving expressions.

What is the relationship between a tangent line and the radius of a circle?

• They are parallel.

• They are perpendicular.

• They do not intersect.

• They intersect at two points.

Which theorem is used to solve problems involving right triangles formed by tangents and radii?

• Cosine Rule

• Triangle Inequality Theorem

• Sine Rule

• Pythagorean Theorem

In a right triangle, if one leg is 15 and the hypotenuse is 18, what is the length of the other leg?

• 9.95

• 12

• 10

• 14

How do you simplify the square root of 99?

• 3√11

• 9√11

• √33

• 11√3

If a right triangle has legs of 10 and x, and a hypotenuse of 20, what is x?

• 15

• 10√3

• 12

• 17.32

What is the simplified radical form of the square root of 300?

• 10√3

• 20√3

• 15√2

• 5√6

In a triangle with a radius of x and a side of 24, what is the expression for the hypotenuse if the other segment is 12?

• x + 24

• x + 12

• x + 36

• x + 18

If the radius of a circle is 16 and the tangent segment is 49, what is the length of the hypotenuse?

• 55

• 65

• 60

• 75

What is the value of x if the equation is set up as x^2 + 63^2 = (x + 49)^2?

• 18

• 16

• 20

• 22

How do you find the circumference of a circle if the radius is x?

• 2πx

• x^2

• πx^2

• πx