Plane geometry

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1899 Excerpt: ...ACB. Then, D is equidistant from AE and BE. Ex. 248. If two equal chords of a circle intersect, their corresponding segments are equal. Ex. 249. If the arc cut off by the base of an inscribed triangle is bisected and from the point of bisection a radius is drawn and also a line to the opposite vertex, the angle between these lines is equal to half the difference of the angles at the base of the triangle. Ex. 250. The two lines which join the opposite extremities of two parallel chords intersect at a point in that diameter which is perpendicular to the chords. Ex. 251. If a tangent is drawn to a circle at the extremity of a chord, the middle point of the subtended arc is equidistant from the chord and the tangent. Ex. 252. A line is drawn touching two tangent circles. Prove that the chords, that join the points of contact with the points in which the line through the centers meets the circumferences, are parallel in pairs. Ex. 253. Two circles intersect at the points A and B; through A a secant is drawn intersecting one circumference in C and the other in D; through B a secant is drawn intersecting the circumference CAB in E and the other circumference in F. Prove that the chords CE and DF are parallel. Suggestion. Eefer to Ex. 198 and 201. Ex. 254. The length of the straight line joining the middle points of the non-parallel sides of a circumscribed trapezoid is equal to one fourth the perimeter of the trapezoid. Ex. 255. A quadrilateral is inscribed in a circle, and two opposite angles are bisected by lines meeting the circumference in A and B. Prove that AB is a diameter. Ex. 256. The centers of the four circles circumscribed about the four triangles formed by the sides and diagonals of a quadrilateral lie on the vertices of a parallelogram. Ex. 257. If a...