# Technical Mathematics Volume 2

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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. 1922 edition. Excerpt: ...the circumference which lies in the line AB. (Definition of a tangent.).'. D lies outside the circle. OD is greater than OC. But a perpendicular is the shortest line that can be drawn from a point to a line. OC must be perpendicular to A B..: A radius drawn to the point of tangency is perpendicular to the tangent. 122. From Theorem XIX it is easily seen that: 1. A line that is perpendicular to a radius at its extrem ity, is tangent to the circle. 2. A line that is perpendicular to a tangent at the point of tangency, passes through the center of the circle. EXERCISE 57 1. Prove: Two tangents to a circle from an external point are equal. (Fig. 165.) 5. Find ZBOA, Fig. 167. 6. The radius of the circle, Fig. 168, is 3 inches. Find the length of the tangent AB. 7. Two tangents are drawn to a 6-inch circle from a point 10 inches from the center. Find the angle between the tangents (see Problem 1). of 73-inch radius..4.8 = 9 inches, AD = 17 inches, BC--17 inches, E and F are the middle points of AB and DC. Find the length of CD and the angles A, B, C, and D. 10. ABCD, Fig. 171, is a regular circumscribed polygon. Fig. 171. The vertices are connected with the center of the circle. Prove that the angles at the center are equal. 11. The side of a regular circumscribed pentagon is 7 inches, Fig. 172. Find the radius of the circle. 12. ABCDE, Fig. 173, is a regular circumscribed pentagon; the radius of the inscribed circle is 7 inches. Find the radius of the circumscribed circle. MEASUREMENT OF ANGLES 123. Inscribed Angle. An inscribed angle is one whose sides are chords of a circle, and whose vertex lies on the circumference of the circle. In Fig. 174, Zs2, A, and B are inscribed angles. By Art. 109, Z1 is measured by the arc AB. The inscribed angle (Z2)...