Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, Ginn & company · leaf 196
Fig. 1.—The point O onthe chord. Fig. 2. —The point O onthe chord produced. Given ABX and AXB, two chords, each divided at 0 intotwo segments. To prove that AO • OBx = AxO • OB. Proof. 1. Suppose AB, AXBX drawn. Then £A = £ Av Why ? 2. .. AB and AXBX are antiparallel, § 251, cor. and .. AO ■ OBx =… … Fig. 3. — The point O atthe end of the chord. FIG. 4. — Chord AXBbecomes zero. Fig. 5. —Chord ABY alsobecomes zero. Corollary. The tangent from the vertex of a pencil to acircumference is a mean proportional between the two segmentsof any other line of the pencil. In Fig. 4, AO ■ BxO=AxO • BO=B02.…
Geometry
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