Angles in Circles Objectives: B GradeUse the tangent / chord properties of a circle. A GradeProve the tangent / chord properties of a circle. Use and prove the alternate segment theorem

Angles in Circles A line drawn at right angles to the radius at the circumference is called the tangent

Angles in Circles O A B P Tangents to a circle from a point P are equal in length: PA = PB OA is perpendicular to PA OB is perpendicular to PB The line PO is the angle bisector of angle APB angle APO = angle BPO The line PO is the perpendicular bisector of the chord AB

Angles in Circles Now do these: a 48 o O b O c 36 o 53 o d a = (180-48) ÷ 2 a = 66 o b = 90 o c = 180-(90+36) c = 54 o d = 360-( ) d = 127 o

Angles in Circles The Alternate Segment Theorem The angle between the tangent and the chord is equal to the angle in the alternate segment

Angles in Circles Now do these: 58 o e 43 o 86 o g e = 58 o 112 o f The angle at the centre is twice that at the circumference 56 o f = 56 o The angle between the tangent and the chord is equal to the angle in the alternate segment 43 o g = g = 129 o

Angles in Circles Now do these: 58 o e 43 o 86 o g e = 58 o 112 o f The angle at the centre is twice that at the circumference 56 o f = 56 o The angle between the tangent and the chord is equal to the angle in the alternate segment 43 o g = g = 129 o

Angles in Circles Worksheet 4 a 48 o O b O c 36 o 53 o d 43 o 86 o g 112 o f 58 o e a = b = c = d = e = f = g =