PROPOSITION XXII 217. Theorem. If a tangent and a secant are drawn from a point to a circumference, the tangent is a mean proportional between the secant and its external seg PROPOSITION XXIII 220. Theorem. If two chords intersect within a circle, the product of the segments of one equals the product of the segments of the other. 221. Theorem. The product of two sides of a triangle equals the product of the diameter of the circumscribed circle and the perpendicular to the third side from the opposite vertex. 222. Cor. The diameter of a circle circumscribed about a triangle equals what? PROPOSITION XXV 223. Theorem. The product of two sides of a triangle equals the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. 177. The sides of similar triangle is 30. 178. The bases of EXERCISES a triangle are 7, 8, and 12. The longest side of a What are the other two sides? two similar triangles are 5 ft. 4 in. and 3 ft. 4 in. The altitude of the first is 4 ft. 10 in. What is the altitude of the second? REGULAR POLYGONS - DEFINITION 224. A Regular Polygon is one that is both equiangular and equilateral. PROPOSITION XXVI 225. Theorem. Regular polygons of the same number of sides are similar. 179. In Prop. XIX, if AC, BC, 23, and 14 are respectively 48, 36, 27, and 25, what are 13 and AD? 180. Two isosceles triangles are similar if any angle of one equals the homologous angle of the other. |