This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ...PB meets QA at R. PAj meets QBj at S. Prove that the points P, Q, R, 6 are concyclic, and that RS is parallel to AAj. 39. If the opposite sides of a cyclic quadrilateral are produced to meet, prove that the bisectors of the angles so formed are at right angles. 40. O is the orthocentre of a triangle ABC. The lute AO ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ...PB meets QA at R. PAj meets QBj at S. Prove that the points P, Q, R, 6 are concyclic, and that RS is parallel to AAj. 39. If the opposite sides of a cyclic quadrilateral are produced to meet, prove that the bisectors of the angles so formed are at right angles. 40. O is the orthocentre of a triangle ABC. The lute AO meets the circum-circle of ABC at D. Prove that OD is bisected at right angles by BC. 41. O is the orthocentre of a triangle ABC. Prove that the circum-circles of ABC, OBC, OCA, OAB are equal. 42. O is the orthocentre, and AAj is a circum-diameter, of the triangle ABC. Prove that OBAjC is a parallelogram, and hence that OAj is bisected at the middle point of BC. 43. O is the orthocentre of a triangle ABC. Prove that AO is double the distance of BC from the circum-centre of the triangle. 44. AD, BE, CF are the perpendiculars from the vertices of a triangle ABC upon its opposite sides. Prove that the orthocentre of ABC is the centre of the circle inscribed in the triangle DEF. The triangle DEF is called the pedal triangle of ABO 45. From any point P on the circum-circle of a triangle ABC perpendiculars PL, PM, PN are drawn upon the sides BC, CA, AB respectively. Prove that the points L, M, N are collinear, that is, they are situated in one straight line. The line LMN is called the Simson Line of the point P. 46. In the preceding exercise, let PL, PM, PN meet the circum-circle again at X, Y, Z respectively. Prove that AX, BY, CZ and the Simson Line of P are parallels. 47. A straight line revolves in a plane about a given point external to itself. Prove that in all positions the straight line touches a fixed circle. 48. From a point P on a fixed circle a tangent PQ, is drawn of given length. What is the locus of the point Q when P moves along the ci...
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Add this copy of A School Course In Geometry: Including The Elements Of to cart. $23.14, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2023 by Legare Street Press.
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Add this copy of A School Course in Geometry: Including the Elements of to cart. $36.26, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2023 by Legare Street Press.
Add this copy of A School Course In Geometry: Including The Elements Of to cart. $45.40, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2023 by Legare Street Press.
All Editions of A School Course in Geometry: Including the Elements of Trigonometry and Mensuration and an Introduction to the Methods of Co-Ordinate Geometry
