Angles Between Tangent and chordObjectives:1.Use the tangent / chord properties of a circle.2.Prove the tangent / chord properties of a circle.

Use and prove the alternate segment theorem

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

Angles in CirclesOABTangents to a circle from a point P are equal in length:PA = PBOA is perpendicular to PAOB is perpendicular to PBThe line PO is the angle bisector of angle APBangle APO = angle BPOThe line PO is the perpendicular bisector of the chord AB

Angles in Circlesa = (180-48) 2a = 66ob = 90oc = 180-(90+36)c = 54od = 360-(90+90+53)d = 127o

Angles in CirclesThe Alternate Segment TheoremThe angle between the tangent and the chord ( a & c) is equal to the angle in the alternate segment ( b & d )bacda = b

c = d

Angles in CirclesNow do these:58oe43o86oge = 58oThe angle at the centre is twice that at the circumference56of = 56oThe angle between the tangent and the chord is equal to the angle inthe alternate segment43og = 43+86g = 129o

Angles in CirclesNow do these:58oe43o86oge = 58oThe angle at the centre is twice that at the circumference56of = 56oThe angle between the tangent and the chord is equal to the angle inthe alternate segment43og = 43+86g = 129o

Angles in CirclesWorksheet 4a = b = c = d = e = f = g =