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Side 149
James Maurice Wilson. We shall now investigate the position of the tangent to a circle at any specified point , using our newly obtained defi- nition of a tangent . the Let A be the point and centre of the circle , and let AK be a ...
James Maurice Wilson. We shall now investigate the position of the tangent to a circle at any specified point , using our newly obtained defi- nition of a tangent . the Let A be the point and centre of the circle , and let AK be a ...
Side 155
... tangent at the point of contact . [ By Theor . 18. ] OBS . ( 1 ) . If the distance between the centres of two circles is greater than the sum of their radii , their circum- ferences will not meet and each circle will be wholly outside ...
... tangent at the point of contact . [ By Theor . 18. ] OBS . ( 1 ) . If the distance between the centres of two circles is greater than the sum of their radii , their circum- ferences will not meet and each circle will be wholly outside ...
Side 158
... tangents at B cannot include an angle but must coincide . EXERCISES . I. If a straight line touch the inner of two concentric circles , and be terminated by the outer , prove that it will be bisected at the point of contact . 2. Any two ...
... tangents at B cannot include an angle but must coincide . EXERCISES . I. If a straight line touch the inner of two concentric circles , and be terminated by the outer , prove that it will be bisected at the point of contact . 2. Any two ...
Side 161
... cut off equal arcs ; and therefore the arcs AD , BD are equal . ( III . 5. ) * Euclid , III . 30 . PROBLEM 3 . To draw a tangent to a circle W. II SECT . VI . ] 161 PROBLEMS . Similarly, MO is the locus of points equidistant from ...
... cut off equal arcs ; and therefore the arcs AD , BD are equal . ( III . 5. ) * Euclid , III . 30 . PROBLEM 3 . To draw a tangent to a circle W. II SECT . VI . ] 161 PROBLEMS . Similarly, MO is the locus of points equidistant from ...
Side 162
... tangent . Secondly , let A be outside the circle . ( Th . 18. ) Construction . Join OA , and on it as diameter describe a circle , cutting the given circle in T and T. Join AT , AT ' ; these shall be tangents from A. Proof . Join OT ...
... tangent . Secondly , let A be outside the circle . ( Th . 18. ) Construction . Join OA , and on it as diameter describe a circle , cutting the given circle in T and T. Join AT , AT ' ; these shall be tangents from A. Proof . Join OT ...
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AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
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