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 95
0XM2 - ME2 = D2 - i?2.Therefore R2 - D2 = ON. EF =2Rr or D2=R2-2Rr, and E2-R2=0lP.EF = 2Rrl or D2 = R2 + 2RrrSimilarly, Ea2 = R2 + 2Rr2 and D32 = R2+2Rr3.Therefore Z>2 + 2)/ + Z>/ + Z>32 = 4#2 + 27^ (r, +r2 + r3-r) = 12£2 by (96). q. e. d. KB. Since the triangles OAN and EEC, and O^Pand… … 66 EXERCISES ON EUCLID [98. 98. To inscribe in a given triangle a parallelogram ofgiven area not exceeding half the given triangle. (See VI.27, 28.) Let ABC be the given triangle, D, E, F the middle points ofits sides, and suppose BGHL the requiredparallelogram. Join FE, ED. Draw CM parallel toAB…
Geometry
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