Chord Length Exploration

Because the distance from the center of a circle to a chord is perpendicular to the chord, we can build a right triangle to d

a. The radius of circle A is 5 units, and the chord BD is 4 units from the center of the circle. How can you build a right triangle to help find the length of the chord? b. Given the radius length and the length of the distance from the center of the circle to the chord, how can you use the Pythagorean Theorem to calculate the length of half of the chord (BC)? What is the full length of the chord BD? c. The radius of circle E is also 5 units. Given that the angle between the radius EF and the distance to the chord (EG) is 30 degrees, how can you use trigonometry to calculate the length of half the chord (FG)? What is the full length of the chord FH?