MATH SOLVE

2 months ago

Q:
# please help i have 2 questions and the second question has 2 answer choices. thank you.

Accepted Solution

A:

Question 1:

The line segment with measure of 14 units is tangent to the circle, meaning that it is perpendicular to the radius.

Thus, we have a right triangle with legs of 14 and x and a hypotenuse of x+10.

Use the Pythagorean theorem to solve for x.

[tex](x+10)^2=x^2+14^2[/tex]

[tex]x^2+20x+100=x^2+196[/tex]

Subtract both sides by x^2

[tex]20x+100=196[/tex]

Subtract both sides by 100

[tex]20x=96[/tex]

Divide both sides by 20

[tex]x=4.8[/tex]

The third choice is your answer.

Question 2:

This question actually has 3 answers.

The answers to this question are the first, second, and fourth choice.

The first choice is correct because this is a property of a tangent line.

The second choice is also correct because this is also a property of the tangent line.

The third choice is incorrect because the tangent line only intersects the radius at the end of the radius.

The fourth choice is correct because that's what a tangent is.

The fifth choice is incorrect because that's actually a property of a secant, not a tangent.

The last choice is incorrect because there are infinitely many lines tangent to a single circle.

The line segment with measure of 14 units is tangent to the circle, meaning that it is perpendicular to the radius.

Thus, we have a right triangle with legs of 14 and x and a hypotenuse of x+10.

Use the Pythagorean theorem to solve for x.

[tex](x+10)^2=x^2+14^2[/tex]

[tex]x^2+20x+100=x^2+196[/tex]

Subtract both sides by x^2

[tex]20x+100=196[/tex]

Subtract both sides by 100

[tex]20x=96[/tex]

Divide both sides by 20

[tex]x=4.8[/tex]

The third choice is your answer.

Question 2:

This question actually has 3 answers.

The answers to this question are the first, second, and fourth choice.

The first choice is correct because this is a property of a tangent line.

The second choice is also correct because this is also a property of the tangent line.

The third choice is incorrect because the tangent line only intersects the radius at the end of the radius.

The fourth choice is correct because that's what a tangent is.

The fifth choice is incorrect because that's actually a property of a secant, not a tangent.

The last choice is incorrect because there are infinitely many lines tangent to a single circle.