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Angles Interior to circles

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.

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Angles Interior to circles

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  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

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