Geometry Basketball Reviewing Circles

Find the arc or angle.

Solution = =60

Find the arc or angle.

Solution 55º Vertical Angles are congruent!

Find the arc or angle.

Solution Semicircle + Arc NB =235

Find the arc or angle.

Solution Inscribed Angle is ½ of its intercepted arc <ABC = ½(84) =42

Find the arc or angle.

Solution Inscribed Angle is ½ its intercepted arc <ABC= ½ (arc AC) 65 = ½ (arc AC) 130 = arc AC

Find the arc or angle.

Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. 135= ½ (MLK) 270 = MLK

Find the arc or angle.

Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. m<1= ½ (260) m<1 = 130

Find the arc or angle.

Solution When the lines intersect IN THE CIRCLE, the angle is the sum of the arcs divided by 2. Wrong arcs  = =130  Sum of correct arcs m<1=130/2 m<1 = 65

Find the arc or angle.

Solution When the lines intersect OUTSIDE THE CIRCLE, the angle is the bigger arc –smaller arc divided by 2. m<1= (122-64)/2 m<1 = 58/2 m<1 = 29

Find the arc or angle.

Solution When the lines intersect OUTSIDE THE CIRCLE, the angle is the bigger arc –smaller arc divided by 2. m<1= (135-55)/2 m<1 = 80/2 m<1 = 40

Find the arc or angle.

Solution When the lines intersect OUTSIDE THE CIRCLE, Outside segmet (whole segment) = Outside segment (whole segment) 8(x+8) = 9 (9) 8(x+8) = 9² 8x+64=81 8x=17 X=17/8

Find the arc or angle.

Solution When the lines intersect OUTSIDE THE CIRCLE, Outside segmet (whole segment) = Outside segment (whole segment) 5(3x+5) = 10 (10) 5(3x+5) = 10² 15x+25=100 15x=75 X=5

Find the center and radius of the circle.

Solution Center : (-3,4) Radius: 6

Find the arc or angle.

Solution m<KMX = 75 Vertical Angles are Congruent!

Find the arc or angle.

Solution Semicircle = = – 165 = 15

Find the arc or angle.

Solution Semicircle + Arc LY

Find the arc or angle.

Solution Inscribed Angle is ½ its intercepted arc m<TUV= ½ (arc TV) m<TUV = ½ (240) m<TUV = 120

Find the arc or angle.

Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. 53= ½ (arcAB) 106 = arc AB

Find the arc or angle.

Solution When the lines intersect IN THE CIRCLE, the angle is the sum of the arcs divided by 2. Use Semicircle  180 – 147 = 33 m<1= (67+33)/2 m<1=100/2 m<1=50

Find the arc or angle.

Solution When the lines intersect ON THE CIRCLE, the angle is ½ of the arc. Use full circle  =210 m<1= ½ (210) m<1=105

Find the arc or angle.

Solution When the lines intersect OUTSIDE THE CIRCLE, the angle is the bigger arc –smaller arc divided by 2. Use full Circle  =126 m<1= ( )/2 m<1 = 108/2 m<1 = 54

Find x.

Solution When the lines intersect IN THE CIRCLE, (part)(part) = (part)(part) (2x)(2x) = (5)(20) 4x²=100 x²=25 x= 5 or -5 (the lengths can’t be negative, so…) x=5

Find x.

Solution When the lines intersect OUTSIDE THE CIRCLE, (part)(part) = (part)(part) (2x)(2x) = (5)(20) 4x²=100 x²=25 x= 5 or -5 (the lengths can’t be negative, so…) x=5

Find x.

Find the angle.