. Elements of geometry : containing books I to III. 3 , and D the given i. It is U off from 5 ABC a tegi Me of ning an l = L I>. Draw the st. line EBF to touch the circle at B. At B make L FBC = L I). Then v the chord B( is drawn from the pt. of contact B, .-. l FBG= i in segment BAC, III. 32. that is, the segment BAC contains an z = _ T>:and .*. a segment has been cut oft from the 3, as was reqd. Q. E. F. Ex. 1. If two circles touch internally at a point, ai ;.line passing through the point will divide the circles inbinents. capable of containing equal ai 2 Ex. 2. Given a side of a tria
. Elements of geometry : containing books I to III. 3 , and D the given i. It is U off from 5 ABC a tegi Me of ning an l = L I>. Draw the st. line EBF to touch the circle at B. At B make L FBC = L I). Then v the chord B( is drawn from the pt. of contact B, .-. l FBG= i in segment BAC, III. 32. that is, the segment BAC contains an z = _ T>:and .*. a segment has been cut oft from the 3, as was reqd. Q. E. F. Ex. 1. If two circles touch internally at a point, ai ;.line passing through the point will divide the circles inbinents. capable of containing equal ai 2 Ex. 2. Given a side of a triangle, its vertical angle, and the radius of the circumscribing circle : construct the triangle. Ex. 3. (liven the base, vertical angle, and the perpendicularfrom the extremity of the base on the opposite side : constructthe triangle. A ( (/.//)S El FMl:\TS. [Book III. Proposition XXXV. tiro chords in a circh cut one another, tfo rectangltained by th segments of om of them, is eq il to the rectanglecontained by the segments of the Let the chords AC, !>!> in the • ABCD intersect in the pt P. Then must reel AP, PC t ct. /;/, PD. From 0, the centre, draw OM, ON I a to AC, BD, and join OA, OB, Then v AC is divided equally in Wand unequally in P, .-. rect. .1 /. PC with sq. Q Ml sq. on .1 M. II. 5, Adding to each the q. on MO, rect. .1 P, PC with sqq. on MP, .W sqq. on AM, MO : .-. rect. .1 /. PO «iili sq. on / =sq. on OA. the Barue way it may be shew n I rect. /./, PD with sq. on OP =sq. on /•.Then V Bq. on OJ =sq. on >li.,-. rect. I/. PC with sq. on OP=rect. /./, PD with Bq. ? ?r. OP; .-. rect .1/ P(7=rect. /;/. /7>. q. b. d. I ?? !. I md /. are fixed points, and two circlesdescribed passing through them; PCQ, PCQ are chorda o|these circles intersecting in C, a point in .1/.: shew tharectangle CP, V is equal to the rectangle 7, CO/. Ex 2. It through any point in the common chord of twocircles, which intersi tiother, there be drawn any two ot
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