Angle AOD 52° as tangent is 90° to the radius (OA), 180 90 3852° – – Angle ABC AOD 2 52 2 26° (as angle subtended at the centre is twice the angle subtended at the circumference). Angle DFE 29° (as tangent is 90° to the radius (OF) or diameter (DF)). Angle EDF 61° (as alternate segments), or as DEF 90° (angle in semicircle is 90°) and 180 (90 + 29) 61° (as there are 180° in a triangle). – Extension AB 26 cm (diameter) so OB 13 cm (radius) as O is the centre of the circle. DE 12 cm as radius bisects chord OD 13 cm as radius Angle DEO is 90° Using Pythagoras’ theorem: OE² OD² DE² – OE² 13² 12² – OE² 169 144 25 – OE 5 The shortest distance is 5 cm
Angle AOD 52° as tangent is 90° to the radius (OA), 180 – 90 – 3852° Angle ABC AOD 2 52 2 26° (as angle subtended at the centre is twice the angle subtended at the circumference). Angle DFE 29° (as tangent is 90° to the radius (OF) or diameter (DF)). Angle EDF 61° (as alternate segments), or as DEF 90° (angle in semicircle is 90°) and 180 – (90 + 29) 61° (as there are 180° in a triangle). Extension AB 26 cm (diameter) so OB 13 cm (radius) as O is the centre of the circle. DE 12 cm as radius bisects chord OD 13 cm as radius Angle DEO is 90° Using Pythagoras’ theorem: OE² OD² – DE² OE² 13² – 12² OE² 169 – 144 25 OE 5 The shortest distance is 5 cm
473509-8.05-circles.docx