Find the value of x given a tangent line to a circle

The video tutorial explains the concept of a tangent line and its properties, including its perpendicular relationship with the radii. It demonstrates how to use the Pythagorean theorem to calculate the value of x in a right triangle formed by the tangent. The tutorial further simplifies the expression for x, showing how to break down the calculation into simpler components and find the exact value using square roots.

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

• They are parallel.

• They form a 90-degree angle.

• They are equal in length.

• They intersect at two points.

Which theorem is used to find the length of a side in a right triangle formed by a tangent and a radius?

• The Tangent-Secant Theorem

• The Law of Sines

• The Law of Cosines

• The Pythagorean Theorem

If one side of a right triangle is 15 and another is 5, what is the length of the hypotenuse?

• Square root of 300

• Square root of 250

• 25

• 20

How can the expression for the hypotenuse length be simplified?

• By adding 10

• By dividing by 5

• By multiplying by 2

• By factoring into 25 times 10

What is the simplified form of the square root of 250?

• 10 times the square root of 10

• 5 times the square root of 10

• 10 times the square root of 5

• 5 times the square root of 5