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acute angle alternate angle equal angled triangle angular points base bisect CANDIDATES centre Certificate chord Christmas circle described circumference common Complete Construct cuts the circle diagonals diameter difference double draw a straight equiangular equilateral triangle Euclid Examinations exercises exterior angle fall figure Find fixed circle four GEOMETRY given circle given point given straight line given triangle greater half the line inscribed interior isosceles triangle length less line be divided line be drawn line drawn line joining London Mathematical MATRICULATION meet middle points Notes obtuse angle opposite angles opposite sides parallel parallelogram pass pentagon perpendicular point of contact problem produced proposition prove quadrilateral questions rectangle contained regular respectively rhombus right angles right-angled triangle Scholarship Section segment side subtending sides containing squares described student taken tangents theorem third third angle touch twice the rectangle unequal vertex whole line Write
Pagina 160 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Pagina 184 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Pagina 156 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Pagina 182 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Pagina 153 - Any two sides of a triangle are together greater than the third side.
Pagina 167 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Pagina 164 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Pagina 130 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.