Tangent in Circle

Is segment AB tangent to this circle?

• Yes

• No

• Not enough information

What kind of angle does this tangent line and radius form?

• Acute

• Obtuse

• Vertical

• Right

Identify the tangent line in the given circle: (x-3)^2 + (y+4)^2 = 25

• The tangent line is perpendicular to the radius

• The tangent line is always a straight line passing through the center of the circle

• The tangent line is parallel to the x-axis

• The tangent line to the circle can be found using the point of tangency and the slope of the radius at that point.

Apply the tangent-secant theorem to find the value of x: The tangent to a circle at point P is parallel to a secant passing through points P and Q. If the length of the secant from P to Q is 12 units and the length of the tangent segment from P to the point of contact with the circle is 8 units, find the value of x.

• 6

• 10

• 4

• 12

Using the properties of tangents, solve for x: Two circles with radii 5 and 8 units are externally tangent to each other. If the distance between their centers is 13 units, find the length of the common external tangent.

• 12

• 5

• 10

• 20

If a tangent to a circle at point A is perpendicular to a radius drawn to the point of contact, what can you conclude about the triangle formed by the tangent, the radius, and the line segment joining the center of the circle to point A?

• Equilateral triangle

• Right-angled triangle

• Obtuse-angled triangle

• Isosceles triangle

Find the length of the tangent segment from a point 10 units away from the center of the circle with a radius of 15 units.

• 12 units

• 25 units

• 17 units

• 5 units

Apply the tangent-secant theorem to find the value of x: The tangent to a circle at point P is parallel to a secant passing through points P and Q. If the length of the secant from P to Q is 20 units and the length of the tangent segment from P to the point of contact with the circle is 12 units, find the value of x.

• x = 16

• x = 10

• x = 25

• x = 8

Using the properties of tangents, solve for x: Two circles with radii 6 and 10 units are externally tangent to each other. If the distance between their centers is 16 units, find the length of the common external tangent.

• 10

• 14

• 8

• 12

Find the length of the tangent segment from a point 5 units away from the center of the circle with a radius of 7 units.

• 2

• 10

• 15

• 24