## Plane Geometry |

### From inside the book

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**Chord**E A**Chord**of a circle is the segment joining any two points of the circle ; as ,**chord**CE . A circle can be drawn with any point as center and any given segment as radius . 17. Two circles having equal radii can be made to ... Page 93

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**chord**of the circle . Suggestion . Compare CD with AO and OB . Also , compare 40+ OB with AB . Ex . 5. If two circles intersect , the distance between their centers is greater than the difference of their radii . A D B 175. From the ... Page 95

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**CHORDS**, ARCS , AND CENTRAL ANGLES 179. Two points on a circle are the ends of two arcs ; a Minor Arc , as AMB , and a Major A Arc , as ANB . Unless the contrary is stated , the minor arc will always be understood when an arc is ... Page 97

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**chord**which subtends the arc . Ex . 17. The twelve spokes of a wheel are spaced so that the points at which they are ...**chord**AB is said to subtend arc AB . Arc AB is said to be subtended by**chord**AB . " Subtend " is derived from ... Page 98

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**chords**are equal , they subtend equal arcs . A B D 3 R Hypothesis . Conclusion . = 0 0 0 R ; AB = CD . Plan . 1 . 2 . AB = CD . Draw AO , OB , RC , RD . Prove ≤ 0 = 2 R , and apply § 181 . [ Proof to be given by the pupil . ] Ex . 18 ...### 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