1 / 14

Secants, Tangents and Angle Measures

Learn how to find angle measures when lines intersect inside or outside a circle. Explore the relationships between secants, tangents, and arcs in various scenarios.

grose
Download Presentation

Secants, Tangents and Angle Measures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Secants, Tangents and Angle Measures • Find measures of angles formed by lines intersecting on or inside a circle. • Find measures of angles formed by lines intersecting outside the circle. Water droplet on a CD

  2. INTERSECTIONS ON OR INSIDE A CIRCLE S B F E D A line that intersects a circle in exactly two points is called a secant. In the figure above, SF and EF are secants of the circle. When two secants intersect inside a circle, the angles formed are related to the arcs they intercept.

  3. Theorem If two secants intersect in the interior of a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. A D 2 1 B C Examples:

  4. Example 1 Secant-Secant Angle Find m2 if mBC = 30 and mAD = 20 B 2 30° A 1 20° C D E

  5. Example 2 Secant-Secant Angle F Find m4 if mFG = 88 and mEH = 76 88° G 4 3 E H 76°

  6. A secant can also intercept a tangent at the point of tangency. Each angle formed has a measure half that of the arc it intercepts. B A D C E

  7. Theorem If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one half the measure of the intercepted arc. B A D C E

  8. Example 3 Secant-Tangent Angle Find the mABC if mAB = 102° 102°

  9. Example 4 Secant-Tangent Angle Find the mRPS if mPT = 114° and mTS = 136° 114° 136°

  10. INTERSECTIONS OUTSIDE A CIRCLE Secants and tangents can also intersect outside a circle. The measure of the angle formed also involves half the measure of the arcs they intercept.

  11. Theorem If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Two Secants Secant-Tangent Two Tangents D D C E B C C B B D A A A

  12. Example 5 Secant-Secant Angle Find x x° 120° 50°

  13. Example 6 Secant-Secant Angle Find x 62° 141° x°

  14. Example 7 Secant-Secant Angle Find x 11° x°

More Related