10.3 Inscribed angles Pg 613. Definitions Inscribed angle- an  whose vertex is on a circle and whose sides contain chords of the circle. Intercepted.

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10.3 Inscribed angles Pg 613

Definitions Inscribed angle- an  whose vertex is on a circle and whose sides contain chords of the circle. Intercepted arc- the arc that lies in the interior of the inscribed angle and has its endpts on the angle A B CD   BD (  BCD

Thm 10.8 measure of an inscribed  If an  is inscribed in a circle, then its measure is ½ the measure of its intercepted arc. m  BAC= ½ m BC A B C (

Example A B C D E m AED= ? ( 180 o

Example A C B D 196 o m  ABD = ? 98 o

Example A B C D 70 o m AD = ? ( 140 o 7x o x = ? 70 = ½ 7x Or 7x = 140 x=20

Thm 10.9 If two inscribed angles of a circle intercept the same arc, then the  s are  W Y C X Z  W   Y

Inscribed Polygon Polygon with ALL vertices on a circle. A B C D ABCD is inscribed in the circle. Circumscribed Circle – the circle around the inscribed polygon.

Thm If a rt. Δ is inscribed in a circle, then the hypotenuse is a diameter of the circle. If one side of an inscribed Δ is a diameter of the circle, then the Δ is a rt. Δ & the  opposite the diameter is the rt. . A B C AC is a diameter. If AC is a diameter, then ΔABC is a rt. Δ AND  B is the rt. .

Ex: find x. PQ is a diameter,   R is a rt. . 3x = 90 0 x = 30 P C Q R3x o

Thm A quadrilateral can be inscribed in a circle iff its opposite  s are supplementary. A B C D m  A + m  C = 180 o m  B +m  D = 180 o So, can a rectangle be inscribed in a circle? Yes, because its opposite  s are supplementary.

Ex: x=? and y=? 85 + x = 180 x = y = 180 y = 100 xoxo yoyo 80 o 85 o

Ex: x=? & y=? 40x+10y=180 22x+19y=180 22x+19(18-4x)=180 22x x= x= x=-162 x=3 10y 19y 22x 40x 4x+y=18 y=18-4x y=18-4(3) y=18-12 y=6 ** Think back to Algebra!

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