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Angles in Circles

Angles in Circles. Objectives: B Grade Use the tangent / chord properties of a circle. A Grade 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

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Angles in Circles

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

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

  3. 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 The line PO is the angle bisector of angle APB B = angle BPO angle APO The line PO is the perpendicular bisector of the chord AB

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

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

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

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

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

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