. The principles of projective geometry applied to the straight line and conic . ual two right angles as do theangles FAD and FED. Therefore FADand CDA are equal and the lines CD andAF are parallel. (6) If a hexagon he circumscribed to a circleand two of the lines joining pairs of oppositevertices pass through the centre, then the liiie join-ing the third pair of opposite vertices also passesth7-ough the centre. Let ABCDEF be a circumscribed hexagon,the sides of which touch the circle as in the figureat A, B, C, D, E, F. Let AD and BE passthrough the centre 0. Join FO, CO. Then the angle FOB =
. The principles of projective geometry applied to the straight line and conic . ual two right angles as do theangles FAD and FED. Therefore FADand CDA are equal and the lines CD andAF are parallel. (6) If a hexagon he circumscribed to a circleand two of the lines joining pairs of oppositevertices pass through the centre, then the liiie join-ing the third pair of opposite vertices also passesth7-ough the centre. Let ABCDEF be a circumscribed hexagon,the sides of which touch the circle as in the figureat A, B, C, D, E, F. Let AD and BE passthrough the centre 0. Join FO, CO. Then the angle FOB = 2. A0B = 2. EOD= EOC;also FOF=EOF and BOC=COC. Therefore, since the angles at 0 arefour right angles, the angle F0C=2 right angles. Therefore FO and OC are in thesame straight line. 10. If two tangents to a circle in-tersect two other tangents in A, A andB, B and 0 be the centre of the circle,then the angles AOA and BOB areequal or supplemental. Let P, Q and T be the points ofcontact of the tangents AS, SA andAA. Then the angle AOT=h angle POTand the angle AOT={ angle TOf^
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
