Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students (1881)
McDowell, James L · Cambridge, Deighton, Bell, and Co. · leaf 48
e for centre and radius equal to halfthe given difference of sides. 24. Given the base and the sum of the two sides of atriangle, find the locus of the foot of the perpendicular fromeither end of the base on the bisector of the external verticalangle. Let ABC be any triangle on the given base BC,… … Draw BH and CG perpendi-cular to HG, and let them be pro-duced to meet the sides producedin F and E. Join DG and DH.Because AG is common to the twotriangles CAG, EAG, and the ad-jacent angles are equal, thereforeCA=AE and CG=GE; therefore BE equals the given sum ofsides, and by (4) DG = \BE;…
Geometry
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