Question

1. What is the relationship of two secants intersecting in the exterior of a circle
to the measures of its intercepted arcs?
2. What is the relationship of a secant and a tangent intersecting in the
exterior of a circle to its intercepted arcs?
3. What is the relationship of two secants intersecting in the interior of a circle
to the measures of the intercepted arcs and its vertical angles?
4. What is the relationship among the segments formed inside a circle when
two secant lines intersect in the interior of a circle?
5. How are the two secants segments drawn from the exterior point to the
circle related to their external secant segments?
6. How about if a tangent segment and a secant segment are drawn to the
circle from an exterior point, what will be its relationship to its segments
formed?​

Answer 1

Answer:

A secant is a line that intersects a circle in exactly two points. When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Answer 2

The relationships between the given components are listed below.

Explanation:

1. When two secants intersect outside a circle then the measure of the angle formed is half of the difference of the measures of the intercepted arcs positively.
2. When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
3. When two secants in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.
4. When two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
5. When two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
6. In this case, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.