. The principles of projective geometry applied to the straight line and conic . Then the circles ofthe coaxal system through L and M will touch Z at these points. (14) A variable circle passes through a fixed point 0 and cuts a given circle in(^, R, and the tangent at 0 meets QR in P. Show that the locus of P is a straightHne. Since PQ. PR = P0- = the square of the tangent from / to the fixed circle, PWoson tlie radical axis of 0 and this circle. Centres of Similitude. (15) If two ciicles touch two other circles, the chords of contact of eithei pairand their radical axis pass through a centre
. The principles of projective geometry applied to the straight line and conic . Then the circles ofthe coaxal system through L and M will touch Z at these points. (14) A variable circle passes through a fixed point 0 and cuts a given circle in(^, R, and the tangent at 0 meets QR in P. Show that the locus of P is a straightHne. Since PQ. PR = P0- = the square of the tangent from / to the fixed circle, PWoson tlie radical axis of 0 and this circle. Centres of Similitude. (15) If two ciicles touch two other circles, the chords of contact of eithei pairand their radical axis pass through a centre of similitude of the other pair. (16) Find a point where three circles subtend equal angles. (17) 0 and C are the centres of two circles and T is one of their centres ofsimilitude. A straight line TRSR8 is drawn to meet the circles in 7i, .S and R\ *S,the points being in the order given. Show that the rectangles TR. TS and TS. TRare equal and constant. (18) The six centres of simiHtude of three circles lie three by three on fourstraight lines termed tlie axes of .
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
