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 218
qual to thesquares on OP and AE, and therefore OP and OE are equal.Therefore the circle with centre 0 and radius OE passes throughP, and cuts the given circles orthogonally. This last method isapplicable to the other two cases. 220. If any secant be drawn through the intersection oftwo tangents to… … Let OA, OB be the tangents, and OGD the secant. Thenshall DA.CB=AC.BD. Because the angle OAC is equal to the angle ADC in thealternate segment (III. 32), therefore the triangles ADO and OACare equiangular, and therefore (VI. 4) AD : DO :: AC : AO; therefore alternately, AD : AC :: DO : AO.…
Geometry
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