jimbo's+9.2

Back to Jimbo's Chapter Nine Tangents and Secants

a line in the plane of a circle can intercet a circle, as in a secant or tangent. a secant is a line that crosses a circle, and therefore connects at two points on the circle. See The Tangent Theorem. An example of a secant is line DC. a tangent runs parallel to the circle's radius and connects at only one point on the circle. An example of a tangent is line AB, which by definition of a tangent, is perpendicular to radius AE.

Radii and Chords Draw a circle and the circles radius

Draw a Chord across the circle, perpendicular to the green radius. Lable the intersection 'z'

Measure the chord on eather side of the intersection 'z'. what do you notice about the chord? The radius cuts the chord in half. No mater where on the circle you draw the chord, there is always a radius that bisects the chord at a right angle. Try this on several other circles to prove the Radius and Chord Theorem.

Now lets say you need to know the length of the chord (without mesuring). for clarity's sake, lets label the diagram.

The radius of the circle (AC) is 5. The length of AB is three. Solve useing the Pythagerean Therem (DB)^2 + 3^2 = 5^2 (DB)^2 = 5 - 3^2 (DB)^2 = 16 DB = 4 Chord ED is 8 by the Radius and Chord Theorem.

Back to Jimbo's Chapter Nine