Modern Geometry |
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Common terms and phrases
ABCD AQ² bisected bisector centre of inversion centre of similitude centroid circle cuts circle having given circle passes circle whose centre circles intersect circumcentre circumcircle coaxal circles coaxal system collinear common chord common tangents concyclic cross-ratio curves cut the circle Definition Describe a circle diagonals diameter divided harmonically equal equicross figure Find the locus fixed circle fixed point four points given circle orthogonally given points harmonic conjugates harmonic pencil harmonic range inscribed limiting points line at infinity line joining medians meets BC mid-point middle point nine-points circle non-intersecting opposite sides orthocentre orthogonal circles pair pedal triangle perpendicular point at infinity point of intersection points of contact polar Prove Ptolemy's theorem quadrilateral radical axis radius ratio respect right angles Show sides BC Simson line subtends system of coaxal tangents three circles touch triangle ABC vertex vertices
Popular passages
Page 82 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 119 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 29 - A line from any vertex of a triangle to the mid-point of the opposite side is called a median of the triangle.
Page 17 - ... the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle, and likewise the external bisector externally. The ratio of the areas of similar triangles is equal to the ratio of the squares on corresponding sides.
Page 24 - A circle which touches one side of a triangle and the other two sides produced, is called an escribed circle of the triangle.
Page 21 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 149 - A straight line meets the sides BC, CA, AB of a triangle in the points P, Q, R respectively; BQ and CR meet at X and AX meets BC at P'.
Page 78 - Plot the locus of a point which moves so that the ratio of its distances from two fixed points remains constant.
Page 43 - Plane geometry (2 hours).— Any three points A', B', C, are taken on the sides BC, CA, AB, respectively, of a triangle ABC. Prove that— (1) the circles circumscribed about the triangles A'B'C, B'C'A. C'A'B meet in a point; (2) the centers of these circumscribed circles are the vertices of a triangle similar to the triangle ABC. Solid geometry (1} hours).
Page 44 - Show that the centres of the four circles which touch the sides of the triangle ABC are at the extremities of diameters of two other fixed circles.