Angles in Circles Objectives B Grade A Grade
Angles in Circles Objectives: B Grade A Grade Use the tangent / chord properties of a circle. Prove 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 Tangents to a circle from a point P are equal in length: PA = PB A OA is perpendicular to PA OB is perpendicular to PB O P B 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 = (180 -48) ÷ 2 a = 66 o a O 48 o b b = 90 o d = 360 -(90+90+53) d = 127 o O c c = 180 -(90+36) c = 54 o 36 o d 53 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: The angle at the centre is twice that at the circumference e = 58 o e f = 56 o f 112 o 58 o 56 o g 43 o The angle between the tangent and the chord is equal to the angle in the alternate segment 86 o o 43 g = 43+86 g = 129 o
Angles in Circles Now do these: The angle at the centre is twice that at the circumference e = 58 o e f = 56 o f 112 o 58 o 56 o g 43 o The angle between the tangent and the chord is equal to the angle in the alternate segment 86 o o 43 g = 43+86 g = 129 o
Worksheet 4 Angles in Circles a c= O 48 o b O b = c 36 o a= e d f 112 o 53 o e= d= 58 o f= g 86 o o 43 g=
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