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  2. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC:

  3. Bisection - Wikipedia

    en.wikipedia.org/wiki/Bisection

    The 'exterior' or 'external bisector' is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles. [1] To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle ...

  4. Constructions in hyperbolic geometry - Wikipedia

    en.wikipedia.org/wiki/Constructions_in...

    Let A' be the intersection of IB' and I'B. Then AA' is the angle bisector of ᗉ IAI'. [3] Case 2b: IB' is parallel to I'B Construct the line segment BB' and using a hyperbolic ruler, construct the line OI" such that OI" is perpendicular to BB' and parallel to B'I". Then, line OA is the angle bisector for ᗉ IAI'. [3]

  5. Pons asinorum - Wikipedia

    en.wikipedia.org/wiki/Pons_asinorum

    Construct the angle bisector of and extend it to meet BC at X. AB = AC and AX is equal to itself. Furthermore, =, so, applying side-angle-side, triangle BAX and triangle CAX are congruent. It follows that the angles at B and C are equal. Legendre uses a similar construction in Éléments de géométrie, but taking X to be the midpoint of BC. [16]

  6. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. [3] [4] The center of an excircle is the intersection of the internal bisector of one angle (at vertex A, for example) and the external bisectors of the other two.

  7. Concurrent lines - Wikipedia

    en.wikipedia.org/wiki/Concurrent_lines

    A convex quadrilateral is ex-tangential if and only if there are six concurrent angles bisectors: the internal angle bisectors at two opposite vertex angles, the external angle bisectors at the other two vertex angles, and the external angle bisectors at the angles formed where the extensions of opposite sides intersect.

  8. DHL plane crash in Lithuania likely due to technical issue ...

    www.aol.com/news/lithuania-leans-towards...

    VILNIUS (Reuters) -Lithuania has found no sign that the crash on Monday of a DHL cargo plane was caused by sabotage, and believes technical issues were a more likely explanation, officials said on ...

  9. Cevian - Wikipedia

    en.wikipedia.org/wiki/Cevian

    In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. [1] [2] Medians and angle bisectors are special cases of cevians.