A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous Examples |
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Page 6
... Limiting Cases . 0 and ∞ . Def . The Angle of intersection of two circles is that between the tangents drawn to them at either point of intersection ; it is therefore equal to the angle between 6 INTRODUCTION . Limiting Cases, 0 and ∞,
... Limiting Cases . 0 and ∞ . Def . The Angle of intersection of two circles is that between the tangents drawn to them at either point of intersection ; it is therefore equal to the angle between 6 INTRODUCTION . Limiting Cases, 0 and ∞,
Page 7
... tangent to the circle at its intersection . EXAMPLES . 1. To find the angles between the circum- and ex - circles of a triangle ABC . [ Since 82 R2 + 2Rr , etc. , we easily obtain 2 cos 01 = with similar expressions for 02 and 03. ] 2 ...
... tangent to the circle at its intersection . EXAMPLES . 1. To find the angles between the circum- and ex - circles of a triangle ABC . [ Since 82 R2 + 2Rr , etc. , we easily obtain 2 cos 01 = with similar expressions for 02 and 03. ] 2 ...
Page 8
... tangent is drawn . According as the X A X T chord AX and angle TAX diminish in magnitude X approaches the tangent . When X is indefinitely near to A , AX is said to have reached its limiting position and may then be considered to ...
... tangent is drawn . According as the X A X T chord AX and angle TAX diminish in magnitude X approaches the tangent . When X is indefinitely near to A , AX is said to have reached its limiting position and may then be considered to ...
Page 9
... tangents . It appears as before that as X approaches A the chord AX and the base angles A and X of the triangle TAX gradu- ally diminish and ultimately vanish . But as the base angles diminish the vertex T approaches the base and a ...
... tangents . It appears as before that as X approaches A the chord AX and the base angles A and X of the triangle TAX gradu- ally diminish and ultimately vanish . But as the base angles diminish the vertex T approaches the base and a ...
Page 11
... tangents to four circles which touch a fifth , due to the late Dr. Casey . B 02 03 04 C A 01 Denote the circle whose ... tangent to the cor- responding circles be 23 . Then 232 = 8232- ( 2-3 ) 2 . or or In the triangle 0020 , we have 23.
... tangents to four circles which touch a fifth , due to the late Dr. Casey . B 02 03 04 C A 01 Denote the circle whose ... tangent to the cor- responding circles be 23 . Then 232 = 8232- ( 2-3 ) 2 . or or In the triangle 0020 , we have 23.
Contents
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Other editions - View all
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland No preview available - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland No preview available - 2018 |
Common terms and phrases
ABCD bisected bisector Brocard points centre of similitude centres of perspective circum-centre circum-circle coaxal system coincide common tangents concurrent concurrent lines conic constant corresponding cyclic polygon cyclic quadrilateral denote diagonals diameter distances equal equation equianharmonic ex-circles fixed point given circles hence hexagon in-circle infinity inscribed inverse points Isogonal Conjugates isosceles limiting points line at infinity lines joining locus maximum mean centre median median triangle meet middle point minimum multiples opposite sides orthocentre orthogonally pair of inverse parallel pedal triangle perpendiculars point of intersection points of contact polar polygon prove r₁ radical axis radius reciprocal rectangle right angles segments sides of ABC similar triangles Similarly Simson lines species squares subtend symmedian point system of points tangents Theorem transversal triangle ABC triangle PQR vertex vertical angle
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