which tool is essential for constructing a tangent line from a point outside the circle?
a. triangle
b. compass
c. ruler
d. protractor
what happens if two tangent lines intersect outside a circle?
a. they are perpendicular to the radius
b. they create congruent segments from the point of intersection to the points of tangency
c. they are parallel
d. they form a right angle
if two tangent segments are drawn to a circle from an external point, what can be said about the segments?
a. they are perpendicular
b. they are equal in length
c. they are parallel
d. they form a right angle
which statement is false about a circles tangent line?
a. it forms a 45 - degree angle with the radius at the point of tangency
b. it never passes through the circles center
c. it forms a perpendicular angle with the radius at the point of tangency
d. it intersects the circle at exactly one point

Question

Accepted Answer

### First Question: Which tool is essential for constructing a tangent line from a point outside the circle?
# Brief Explanations:
To construct a tangent from an external point, we need to find the equal - length tangents. A compass is used to draw arcs and circles, which is essential for finding the points of tangency. A triangle is not used for this construction, a ruler is for drawing straight lines but not for the geometric construction of the tangent, and a protractor is for measuring angles, not for constructing the tangent.
# Answer:
b. Compass

### Second Question: What happens if two tangent lines intersect outside a circle?
# Brief Explanations:
By the tangent - segment theorem, if two tangent lines are drawn from an external point to a circle, the lengths of the two tangent segments (from the external point to the points of tangency) are equal. Option a is about a single tangent and radius, option c is wrong as tangents from an external point are not parallel, and option d is wrong as they don't necessarily form a right angle.
# Answer:
b. They create congruent segments from the point of intersection to the points of tangency

### Third Question: If two tangent segments are drawn to a circle from an external point, what can be said about the segments?
# Brief Explanations:
The tangent - segment theorem states that if two tangent segments are drawn from an external point to a circle, then the two tangent segments are equal in length. They are not perpendicular (option a), not parallel (option c), and do not form a right angle (option d) in general.
# Answer:
b. They are equal in length

### Fourth Question: Which statement is FALSE about a circle’s tangent line?
# Brief Explanations:
A tangent to a circle is perpendicular to the radius at the point of tangency, so it forms a 90 - degree angle, not a 45 - degree angle (option a is false). A tangent does not pass through the center (option b is also false? Wait, no, the main false one here: The tangent is perpendicular to the radius at the point of tangency, so it makes a 90 - degree angle, not 45 - degree. Also, a tangent does not pass through the center. But among the options, option a says it forms a 45 - degree angle with the radius at the point of tangency, which is false. Option b: A tangent does not pass through the center, so that's also false? Wait, let's re - check. The tangent line touches the circle at exactly one point and is perpendicular to the radius at that point. So:
- Option a: False, because it should be 90 degrees, not 45.
- Option b: False, tangent does not pass through the center.
- Option c: True, it is perpendicular to the radius at the point of tangency.
- Option d: True, it intersects the circle at exactly one point.

But maybe there is a typo in the option b (maybe "It never passes through the circle’s center" was intended? If we assume that, then option a is false. Since the question is about which is false, and the key property is that tangent is perpendicular (90 degrees) to radius, so option a is false.
# Answer:
a. It forms a 45 - degree angle with the radius at the point of tangency

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QUESTION IMAGE

Question

Explanation:

First Question: Which tool is essential for constructing a tangent line from a point outside the circle?

Answer:

Second Question: What happens if two tangent lines intersect outside a circle?