# Mathematics for Shop and Drawing Students

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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. 1921 edition. Excerpt: ...Passes through the center of the circle. (b) Bisects the chord. (c) Is perpendicular to the chord. (d) Bisects the arc. 6. A tangent to a circle is perpendicular to the radius drawn to the point of tangency (Fig. 92), and conversely. 7. Arcs included between parallel lines are equal. CIRCLE THEOREMS 99 8. An inscribed angle is measured by one-half the intercepted arc (Fig. 93). 9. An angle formed by a tangent and a chord Fig. (94) is measured by one-half the intercepted arc. 10. An angle formed by two secants meeting outside a circle (Fig. 95) is measured by one-half the difference of the intercepted arcs. 11. Two tangents drawn to a circle from an external point (Fig. 96) are equal. 80, Ratio and Proportion. 1. If two quantities are in proportion the product cf the extremes equals the product of the means: i.e., if a: b:: c: d, then ad = bc. 2. A line parallel to one side of a triangle divides the other two sides proportionally. 3. The medians of a triangle meet in a point two-thirds of the distance from the vertex to the mid-point of the opposite side. 4. The bisector of the angle of a triangle (Fig. 97) divides the opposite side into segments proportional to the Fig. 97. adjacent sides. 81. Similar Triangles. Triangles having their sides proportional and angles equal are similar. 1. Two triangles are similar if two angles of the one are equal to two angles of the other. 2. Two triangles are similar if the three sides of the one are proportional to the three sides of the other. 3. Triangles having their corresponding sides parallel or perpendicular are similar. 82. Right Triangles. 1. Two right triangles having an acute angle of the one equal to an acute angle of the other are similar. 2. The square on the hypotenuse of a right triangle is equal