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ABē altitude base bisects centre chord circles touch circumference circumscribed common tangent concyclic Construct corresponding sides cyclic quadrilateral Describe a circle diagonals diagram diameter divided draw a st EFGH equal in area equiangular polygon equidistant equilateral exterior figure Find a point Find the locus fixed points given circle given point given st given straight line gm ABCD hypotenuse Hypothesis Hypothesis.-ABC inches inscribed circle isosceles KLMN length line drawn line joining mean proportional median drawn middle point opposite sides parallelogram perpendicular point of contact point of intersection polygon produced Proof Prove radius rect rectangle contained respectively equal rhombus right bisector secant segment Show sides equal similar square subtend tangent THEOREM triangle vertex vertices
Page 130 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Page 241 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Page 254 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 253 - When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other...
Page 235 - Plot the locus of a point which moves so that the ratio of its distances from two fixed points remains constant.
Page 122 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 66 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.