Question

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Prove the Intersecting Secants Theorem: Given a circle with chords AB and CD. if the lines AB and CD intersect at a point, E, that lies outside of the circle, as il- lustrated in Figure 10.30, prove that EA - EB = EC · ED. [Notice that, unlike the Intersecting Chords Theorem, here EA and EB are overlapping segments, as are EC and ED.]

Answer 1

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LADC are 2ABC amd here See AC arc Same ADe 20 LABC 120-LABC 120-AD c ZADE CBE 4 CBE haNe and We fers 4 ADE CDEA= BEC same arple) Cshotwn LADE LCBE KDAE = BCE because md 180-(DEA+ L ADE 180-CLBE C LeBE 4 ADE N 4CBE 14ence ori te Hence we can ED E A E C E D EC E A GL