Understanding Tangents and the Pythagorean Theorem

This video tutorial explains how to solve for unknown values using the properties of a tangent to a circle. It begins with a review of the tangent property, which states that a line is tangent to a circle if it is perpendicular to the radius at the point of tangency. The tutorial then provides two examples. The first example demonstrates solving for a side length in a right triangle using the Pythagorean theorem. The second example involves solving for the hypotenuse of a right triangle, again using the Pythagorean theorem. The video emphasizes understanding the geometric properties and applying the theorem to find unknown values.

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

• They form an acute angle.

• They are parallel.

• They are equal in length.

• They are perpendicular.

In the first example, what theorem is used to solve for the unknown value?

• The Law of Sines

• The Law of Cosines

• The Pythagorean Theorem

• The Tangent-Secant Theorem

What is the value of 24 squared, as used in the first example?

• 576

• 484

• 529

• 625

How is the square root of 176 simplified in the video?

• By using a calculator

• By estimating

• By identifying perfect square factors

• By dividing by 2

Which of the following is a perfect square factor of 176?

• 36

• 25

• 16

• 9

In the second example, what is the unknown value being solved for?

• A leg of the triangle

• The hypotenuse

• The radius

• The tangent segment

What is the sum of 64 and 225 in the second example?

• 298

• 289

• 2890

• 2899

What is the square root of 289, as shown in the second example?

• 15

• 16

• 17

• 18

Which number is confirmed as a perfect square in the conclusion?

• 225

• 196

• 256

• 289

What is the final simplified value of x in the second example?

• 16 units

• 17 units

• 15 units

• 18 units