Exploring Tangent and Secant Segment Lengths

What is the measure of an angle in an isosceles triangle if the vertex angle is 70 degrees?

• 110 degrees

• 55 degrees

• 70 degrees

• 35 degrees

How is the measure of an inscribed angle related to its intercepted arc?

• It is half the measure of the intercepted arc.

• It is unrelated to the intercepted arc.

• It is equal to the measure of the intercepted arc.

• It is twice the measure of the intercepted arc.

In a cyclic quadrilateral, if one angle is 110 degrees, what is the measure of the opposite angle?

• 70 degrees

• 110 degrees

• 140 degrees

• 90 degrees

What is the relationship between the exterior segment and the whole segment of a secant in circle geometry?

• There is no specific relationship.

• The sum of the exterior segment and the whole segment is constant.

• The product of the exterior segment and the whole segment is constant.

• The difference between the exterior segment and the whole segment is constant.

What is the result when a tangent and a secant intersect outside a circle?

• The square of the tangent segment equals the product of the secant's exterior and whole segments.

• The square of the tangent segment equals the sum of the secant's exterior and whole segments.

• The tangent segment equals the secant's exterior segment.

• The tangent segment equals the secant's whole segment.

When solving for an unknown in a circle geometry problem involving secants, what mathematical operation is primarily used?

• Addition

• Multiplication

• Division

• Subtraction

How do you find the measure of an angle formed by two secants intersecting outside of a circle?

• Divide the measure of the larger intercepted arc by the smaller.

• Subtract the measures of the intercepted arcs and divide by 2.

• Add the measures of the intercepted arcs and divide by 2.

• Multiply the measures of the intercepted arcs and divide by 2.

If two tangents from the same point outside a circle are drawn to the circle, how do their lengths compare?

• The lengths are equal.

• The lengths cannot be determined.

• The lengths are proportional to the radii.

• The lengths are inversely proportional.

What is the perimeter of a triangle formed by two tangents and a line segment connecting the points of tangency, if the tangents are 5 cm, 4 cm, and 3 cm respectively?

• 24 cm

• 20 cm

• 12 cm

• 22 cm

In a circle, if a radius is drawn to a point of tangency, what type of angle is formed?

• A straight angle

• An acute angle

• An obtuse angle

• A right angle