## Plane Geometry |

### From inside the book

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Page 162

... tangents . A straight line which is tangent to each of two circles is called a common tangent of the circles . A B D ∞ C If the circles lie on the same side of the common tangent , it is called a common

... tangents . A straight line which is tangent to each of two circles is called a common tangent of the circles . A B D ∞ C If the circles lie on the same side of the common tangent , it is called a common

**external tangent**, as AB . If ... Page 163

... tangent . 5. Draw two circles which have no common tangent . 6. Prove that the common

... tangent . 5. Draw two circles which have no common tangent . 6. Prove that the common

**internal tangents**of two ... INTERNALLY ∞ TANGENT EXTERNALLY Two circles are said to be tangent internally when they lie on the same side of the ... Page 164

... tangent to each other , the point of contact lies on the line of centers . ж B Hypothesis . Circles with centers A ...

... tangent to each other , the point of contact lies on the line of centers . ж B Hypothesis . Circles with centers A ...

**internally tangent**. 4. Two circles are tangent externally at A , and also have a common tangent touching them ... Page 165

... tangent touching them at B and C , respectively , a circle with diameter BC ...

... tangent touching them at B and C , respectively , a circle with diameter BC ...

**internal tangent**of two equal circles bisects the line of centers . 9. If ... tangents to a circle , two of which , AD and AE , are fixed , while the ... Page 166

...

...

**tangents**is a circle . 18. What is the locus of the centers of all circles with a given radius r and**tangent**externally or**internally**to a given circle ? Prove the answer . 19. The adjoining figure is used much in different decorative ...### Other editions - View all

### Common terms and phrases

AABC ABCD AC and BD acute angle altitude angle equal angles are equal apothem base bisects central angle chord circle with center circumscribed compasses and straightedge Conclusion congruent Construct a triangle Corollary corresponding sides decagon diagonals diameter distance Divide a given drawn equal angles equal arcs equal circles equidistant equilateral triangle EXERCISES exterior angles follows formed geometry given angle given circle given line given line-segment given point given triangle Hence hypotenuse Hypothesis inscribed angle intercepted internally tangent intersect isosceles triangle locus measure medians middle points number of sides parallel lines parallelogram perimeter perpendicular bisector point of contact proof in full proof is left quadrilateral radii radius ratio rectangle regular polygon rhombus right angle right triangle secant segment Show similar polygons square straight angle straight line student SUGGESTION tangent trapezoid vertex Write the proof

### Popular passages

Page 130 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 76 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 223 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.

Page 4 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.

Page 21 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.

Page 222 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 131 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 72 - There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.

Page 258 - S' denote the areas of two circles, R and R' their radii, and D and D' their diameters. Then, I . 5*1 = =»!. That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.

Page 197 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.