Circle Theorems Geometry

Theorem:

• Angle between tangent and chord - Acute angle

• Angle between tangent and chord - Obtuse angle

• Tan chord theorem - Acute angle

• Tan chord theorem - Obtuse angle

Tags

CCSS.HSG.C.A.2

Line ABC represents:

• Chord

• Tangent

• Radius

• Diameter

Line FG represents

• Tangent

• Radius

• Chord

• Diameter

Tags

CCSS.HSG.C.A.2

Theorem statement

• Line perpendicular to chord

• Perpendicular bisector of chord

• Line from centre perpendicular to chord

• Line thru centre and midpoint

AC = __ units

• 8

• 16

• 12

• 20

y =

• 23

• 46

• 180 - 23

• 11,5

Tags

CCSS.HSG.C.A.2

x =

• 30

• 90

• 60

Tags

CCSS.HSG.C.A.2

x = ? and y = ?

• x= 20 and y = 15

• x = 15 and y = 20

• x = 20 and y = 20

• x = 15 and y = 15

Tags

CCSS.HSG.C.A.2

x = ? and y = ?

• x = 80 and y = 70

• x = 110 and y = 100

• x = 100 and y = 110

• x = 70 and y = 80

x = ?

• = 106 (opp < of cyclic quad)

• = y = 106 (alt <s =, AD // BC and ext < of cyclic quad)

• = y = 106 (opp < of cyclic quad)

• = y = 106 (ext < of cyclic quad)