Understanding Tangents and Circles

What is the condition for two circles to be externally tangent?

• Their centers are inside each other.

• They have two intersection points.

• Their centers are outside each other with one intersection point.

• They do not intersect at all.

How is a common external tangent different from a common internal tangent?

• A common external tangent does not intersect the line joining the centers.

• A common internal tangent does not intersect the line joining the centers.

• Both tangents intersect the line joining the centers.

• A common external tangent intersects the line joining the centers.

What is true about a line tangent to a circle at a point?

• It is parallel to the radius at the point of tangency.

• It is perpendicular to the radius at the point of tangency.

• It is equal in length to the radius.

• It forms an acute angle with the radius.

If two tangents are drawn from a point outside a circle, what can be said about them?

• They are parallel.

• They are perpendicular.

• They are congruent.

• They are unequal.

In the example where AB is tangent to Circle C at point B, what is the value of x if AD is also tangent to Circle C at point D?

• x = 10

• x = 5

• x = 25

• x = 49

What theorem is used to find the length of a common external tangent between two circles?

• Congruent Triangles Theorem

• Pythagorean Theorem

• Tangent-Secant Theorem

• Circle Theorem

In the example with circles P and Q, what is the length of the common external tangent AB?

• 8

• 4√3

• 12

• 6

What is the first step in finding the radius of a circle inscribed in a triangle?

• Find the area of the triangle.

• Calculate the perimeter of the triangle.

• Draw the altitude of the triangle.

• Identify the hypotenuse.

When setting up proportions to find the radius of an inscribed circle, what is compared?

• The radius and the altitude

• The hypotenuse and the base

• The altitude and the base

• The radius and the hypotenuse

What is the simplified form of the radius of the inscribed circle in the example given?

• 3√247/17

• 3√247/13

• 3√247/19

• 3√247/23