Understanding Right Triangles and the Pythagorean Theorem

The video tutorial explains how to determine the length of a segment, x, in a geometric diagram involving a circle with a radius of 3√6 cm and a segment of 2 cm. By forming a right triangle with the circle's radius as the hypotenuse, the Pythagorean theorem is applied to solve for x. The process involves setting up the equation x² + 2² = (3√6)², simplifying it to x² + 4 = 54, and solving for x to find that x equals 5√2 cm. The tutorial concludes with a recap of the solution and its geometric significance.

What is the radius of the circle given in the problem?

• 6 cm

• 3 cm

• 3√6 cm

• √6 cm

How long is the segment that is perpendicular to the radius in the diagram?

• 3 cm

• 3√6 cm

• 2 cm

• 6 cm

Which theorem is used to determine the value of x in the right triangle?

• Pythagorean Theorem

• Cosine Rule

• Sine Rule

• Thales' Theorem

What is the equation formed using the Pythagorean theorem for this problem?

• x^2 + 2^2 = 3^2

• x^2 + 3^2 = (2√6)^2

• x^2 + 2^2 = (3√6)^2

• x^2 + 3^2 = 2^2

What is the value of 3√6 squared?

• 72

• 36

• 18

• 54

After simplifying the equation, what is x squared equal to?

• 52

• 48

• 54

• 50

What is the principal square root of 50?

• 10

• √25

• 5√5

• 5√2

Why do we only consider the positive solution for x?

• Because x is a length and cannot be negative

• Because the negative solution is incorrect

• Because the problem specifies a positive solution

• Because the circle is in the first quadrant

What is the final value of x in the context of the problem?

• 5

• 5√2

• 2√5

• 10

What does the value of x represent in the right triangle?

• One leg of the triangle

• The radius of the circle

• The hypotenuse

• The diameter of the circle