241. The Book of Lemmas: Proposition 3

The Book of Lemmas: Proposition 3. Let P be any point on a segment of a circle whose base is AB, and let PN be perpendicular to AB. Take D on AB so that AN ND. If now PQ be an arc equal to the arc PA, and BQ be joined, then BQ, BD shall be equal
URL: http://www.cut-the-knot.org/Curriculum/Geometry/BookOfLemmas/BOL3.shtml - 29kb - 19 Jun 2006

242. The Book of Lemmas: Proposition 5

The Book of Lemmas: Proposition 5. Let AB be the diameter of a semicircle, C any point on AB, and CD perpendicular to it, and let semicircles be described within the first semicircle and having AC, CB as diameters. Then if two circles be drawn touching CD on different sides and each touching two of the semicircles, the circles so drawn will be equal.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/BookOfLemmas/BOL5.shtml - 29kb - 19 Jun 2006

243. Carpets Theorem

Carpets Theorem
URL: http://www.cut-the-knot.org/Curriculum/Geometry/CarpetsInSquare.shtml - 29kb - 19 Jun 2006

244. Two Butterflies Theorem

Two Butterflies Theorem
URL: http://www.cut-the-knot.org/Curriculum/Geometry/TwoButterflies.shtml - 30kb - 19 Jun 2006

245. The Book of Lemmas: Proposition 10

The Book of Lemmas: Proposition 10. Suppose that TA, TB are two tangents to a circle, while TC cuts it. Let BD be the chord through B parallel to TC, and let AD meet TC in E. Then, if EH be drawn perpendicular to BD, it will bisect it in H.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/BookOfLemmas/BOL10.shtml - 30kb - 19 Jun 2006

246. The Eyeball Theorem

The Eyeball Theorem: tangents from the centers of two circles to the other circle cut equal segments on the circles of origin
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Eyeball.shtml - 30kb - 19 Jun 2006

247. Three Tangents Theorem

Three Tangents Theorem
URL: http://www.cut-the-knot.org/Curriculum/Geometry/3Tangents.shtml - 30kb - 19 Jun 2006

248. Remarkable Line in Cyclic Quadrilateral

Remarkable Line in Cyclic Quadrilateral: might be called Euler's line
URL: http://www.cut-the-knot.org/Curriculum/Geometry/InscribedQuadri.shtml - 30kb - 19 Jun 2006

249. Soddy Circles and David Eppstein's Centers

Soddy Circles and David Eppstein's Centers: four circles that touch pairwise in six points. Those points, taken pairwise, define three concurrent lines
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Eppstein.shtml - 32kb - 19 Jun 2006

250. The Book of Lemmas: Proposition 12

The Book of Lemmas: Proposition 12. If AB be the diameter of a semicircle, and TP, TQ the tangents to it from any point T, and if AQ, BP be joined meeting in R, then TR is perpendicular to AB.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/BookOfLemmas/BOL12.shtml - 32kb - 19 Jun 2006

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