Chords and Secant Relationships

Name Computer Number

Construct two chords intersecting inside a large circle. Begin by selecting the circle and putting four points on the object (from the construct menu). Select your two points at at a time and construct the chords. Record the measurements.

r = t =

s = u =

r X s = t XX u =

If two chords intersect in a circle, then the products of the measures of the segments of the chords are

.

Drag one of the chords around the circle slowly to see if any of your statements hold true.

Write the relationship algebraically using the given variable: .

Find r if s = 6, u = 10, and t = 3. (show all work).

Find x if s = x, r = 8 - x, t = 4, and u = 3. (show all work).

Construct two secant segments to a circle from a common external point.

Let r and t be the entire secant segment, but s and u be only the outside part. To do this you must construct points of intersections between the secants and the circle and then construct segments from these points and the external point.

r = t =

s = u =

r X s = t XX u =

If 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 to the product of the measures of the other secant segment and its external secant segment.

Drag parts of the diagram to see if any of your conclusion holds true.

Express the relationship algebraically: .

Find r if s = 8, r = x, t = 12, and u = 4. (show all work).

Find x if u = 5, s = 6, t - u = 7, and r - s = x. (show all work).

Construct a tangent segment and a secant segment to a circle from a common external point. Let r be the entire tangent length, s be the entire secant length, but t be the outside part of the secant segment.

r = s = t = r x r = s x t =

If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the measure of the tangent is to the product of the measures of the secant segment and its external secant segment.

Drag parts of the diagram to see if your conclusion holds true.

Find t if r = 12 and s = 16. (show all work)

Find r if s = 15 and t = 9. (show all work)