1 / 11

Angles Interior to circles

This text explores the concept of angles subtended by segments or arcs in circles. It explains how inscribed angles, such as angle BAC formed by arc BC, relate to segments. The document covers two main theorems: the measure of an angle created by a tangent and a chord is half the measure of the corresponding arc, and the angle formed by two intersecting chords equates to half the sum of the intersected arcs. Examples illustrate how to find angle measures when given specific chord and arc values.

nhung
Télécharger la présentation

Angles Interior to circles

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. Angles Interior to circles A segment or arc is said to subtend an angle if the endpoints of the segments or arc lie on the sides of the angle. Inscribed angles are one type of subtended angle. < BAC is subtended by arc BC or segment BC

  2. Another type of subtended angle is one formed by a tangent to the circle and a chord of the circle

  3. Theorem 64-1 • The measure of an angle formed by a tangent and a chord is equal to half the measure of the arc that subtends it. • m<ACD = 1/2 m arc AC 140o D

  4. Finding angle measures with tangents and chords • Find a<ABC Find arc BC A B 76o B C 30o A C

  5. Theorem 64-2 • The measure of an angle formed by 2 chords intersecting in a circle is equal to half the sum of the intersected arcs. • m<1 = 1/2 (m arc EF +m arc GH) • m<2= 1/2 (m arc EG and m arc FH) G E 1 2 H F

  6. Finding angle measures of intersecting chords 70o x 180o

  7. Find arc AC

  8. Find angle x

  9. Find x 45o 59o x

More Related