Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 91
... secants are drawn terminating in the concave arc , and if the line joining the center of the circle with the given point bisects the angle formed by the secants , the secants are equal . 288. EXERCISE . If two chords intersect in a ...
... secants are drawn terminating in the concave arc , and if the line joining the center of the circle with the given point bisects the angle formed by the secants , the secants are equal . 288. EXERCISE . If two chords intersect in a ...
Seite 94
... secants , terminating in the circumference , can be drawn . - Suggestion . — Suppose that three equal secants could be drawn . Using the given point as a center and the length of the secant as a radius , describe a circle . Apply § 299 ...
... secants , terminating in the circumference , can be drawn . - Suggestion . — Suppose that three equal secants could be drawn . Using the given point as a center and the length of the secant as a radius , describe a circle . Apply § 299 ...
Seite 116
... secants meeting without the circle is measured by one half the difference of the arcs intercepted by its sides . A E B Let 1 be an angle formed by the two secants AB and CB . To Prove 21 ~ 1 ( AC — DE ) . Proof . Draw the chord CE . Z1 ...
... secants meeting without the circle is measured by one half the difference of the arcs intercepted by its sides . A E B Let 1 be an angle formed by the two secants AB and CB . To Prove 21 ~ 1 ( AC — DE ) . Proof . Draw the chord CE . Z1 ...
Seite 117
Alan Sanders. 384. EXERCISE . If the secants AB and CB in the figure of § 383 intercept arcs of 70 ° and 42 ° , what ... secant meet- ing without the circle is measured by one half the dif- ference of the arcs intercepted by its sides . 0 ...
Alan Sanders. 384. EXERCISE . If the secants AB and CB in the figure of § 383 intercept arcs of 70 ° and 42 ° , what ... secant meet- ing without the circle is measured by one half the dif- ference of the arcs intercepted by its sides . 0 ...
Seite 122
... secants , AB and AC , are drawn to the circle , and AB passes through the center . Prove AB > AC . D B 2. One angle of an inscribed triangle is 42 ° , and one of its sides subtends an arc of 110 ° . Find the angles of the triangle . 3 ...
... secants , AB and AC , are drawn to the circle , and AB passes through the center . Prove AB > AC . D B 2. One angle of an inscribed triangle is 42 ° , and one of its sides subtends an arc of 110 ° . Find the angles of the triangle . 3 ...
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Häufige Begriffe und Wortgruppen
AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc ABC arcs intercepted BC² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point homologous homologous sides hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ΔΑΒΟ ᎠᏴ
Beliebte Passagen
Seite 68 - 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.
Seite 163 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Seite 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Seite 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Seite 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Seite 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Seite 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Seite 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Seite 11 - 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.
Seite 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.