# 9.2 Chord Properties

## Investigation 1

1. Use the distance tool to measure BC and DE.
2. Use the distance tool to measure the arcs intercepted by BC and DE (in bold).
3. Use the angle tool to measure central angles BAC and DAE.
4. Use the arrow tool to drag B and D around the circle. Observe what happens to the measures.

## C76- Chord Central Angles Conjecture

What is the relationship between the central angles determined by congruent chords on a circle?

## C77- Chord Arcs Conjecture

What is the relationship between the arcs intercepted by congruent chords on a circle?

## Investigation 2

1. Use the distance tool to measure BC and DE.
2. Use the perpendicular line tool to construct a perpendicular line from point A to BC.
3. Use the point tool to construct a point where the perpendicular line intersects BC.
4. Use the distance tool to measure the distance from B to the intersection point and from C to the intersection point.
5. Use the perpendicular line tool to construct a perpendicular line from A to DE, construct a point where they intersect, and measure the distances from D and E to that point of intersection.
6. Use the distance tool to measure the distances from A to each of the intersection points on the chords.
7. Use the arrow tool to drag points D and B around the circle. Observe how the measures change.

## C78- Perpendicular to a Chord Conjecture

At what point does a perpendicular line from the center of a circle to a chord intersect the chord?

## C79- Chord Distance to Center Conjecture

What is the relationship between the distances from the center of a circle to 2 congruent chords on the circle?

## Investigation 3

1. Use the perpendicular bisector tool to construct the perpendicular bisector for each of the chords on the circle.
2. Use the arrow tool to drag endpoints of the chords around the circle. It's ok if the chords overlap. Observe how the perpendicular bisectors move.

## C80- Perpendicular Bisector Chord Conjecture

What point do all perpendicular bisectors of chords on a circle pass through?