## Plane Geometry |

### From inside the book

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**tangent**to a circle is a straight line which touches the circle at only one point . Χ The circle is also said to be**tangent**to the line . B The point where the**tangent**touches the circle is called the Point of Tangency , or Point of ... Page 105

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**tangent**to the circle . E A D D B Hypothesis . OC is a radius of OO ; AB LOC at C. Conclusion . Proof . 1 . 2 . 3 . 4 . 5 . AB is**tangent**to O 0 . Let D be any point in AB except C. Draw OD . .. OD > OC . .. point D lies outside of ... Page 106

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**tangents**to 0 . Conclusion . AB = AC . [ Proof to be given by the pupil . Recall § 114. ] Note . - The proof of Prop . XIV is attributed to a mathematician Fink , with the ...**tangent**to each of two circles 106 PLANE GEOMETRY BOOK II. Page 107

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**tangent**. If the circles lie on the same side of AB , AB is called a common ex- ternal**tangent**. The length of a common**tangent**is the length of the segment between the two points of contact . Some uses of common**tangents**are ... Page 108

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**tangent**to AB at A. OO ' is the line of centers . St. line 00 ' passes through A. Draw the radii OA and O'A ...**tangent**externally . As an optional exercise , it is suggested that the theorem be proved when the are**tangent**...### Other editions - View all

### Common terms and phrases

ABCD acute angle adjacent angles adjoining figure altitude angles are equal apothem base bisector bisects central angle chord circle of radius circumscribed polygons Conclusion congruent Construct a triangle Determine diagonals diameter divide Draw drawn equal angles equal circles equal respectively equal sides equidistant equilateral triangle extended exterior angle geometry given circle given point given segment given triangle Hence homologous sides hypotenuse Hypothesis intersect isosceles trapezoid isosceles triangle length mean proportional median meeting AC mid-point Note number of sides opposite sides parallel parallelogram pentagon perigon perimeter perpendicular perpendicular-bisector PROPOSITION quadrilateral radii ratio rectangle regular inscribed polygons regular polygon rhombus right angle right triangle secant similar triangles straight angle straight line Suggestion Suggestions.-1 Supplementary Exercises tangent THEOREM trapezoid triangle ABC triangle equal Try to prove vertex ZAOB

### Popular passages

Page 166 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Page 207 - The areas of two similar triangles are to each other as the squares of any two homologous sides.

Page 166 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Page 83 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.

Page 170 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 105 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Page 86 - If two triangles have two sides of one equal, respectively, to two sides of the other...

Page 204 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 299 - Prove that an equiangular polygon inscribed in a circle is regular if the number of sides is odd. Ex.

Page 194 - Two rectangles are to each other as the products of their bases and altitudes. For if R = a6, and R