We learned rules for the measures of angles and segments formed by intersecting chords, secants, and tangents in a circle…
- If two chords or secants to the same circle intersect inside the circle, the measure of the angle formed is half the sum of the measures of the two intercepted arcs.
- If two secants (or two tangents, or a secant and a tangent) to the same circle intersect outside the circle, the measure of the angle formed is half the difference of the measures of the two intercepted arcs.
- If two chords intersect inside a circle, the product of the measures of the two segments of one chord equals the product of the measures of the two segments of the other chord.
- If two secant segments intersect outside a circle, the product of one secant segment measure and its external segment measure equals the product of the other secant segment measure and its external segment measure.
- If a secant segment and a tangent segment intersect outside a circle, the square of the tangent segment measure equals the product of the secant segment measure and its external segment measure.
Whew! Obviously, these rules made a lot more sense when seen in the context of example problems. I hope you took notes on the sample problems we worked in class!
Homework #4H11: 20110419 Geom HW – Segment and Angle Measures in Circles, all problems. (*This document is not the same one you received in class, but it contains the same type and number of problems.)