New Plane And Solid Geometry

Cover New Plane And Solid Geometry
New Plane And Solid Geometry
Webster Wells
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1. If c is chord 6. (§ 166) 2. If c = d, chord a will equal chord 6. (§ 165) 3. Both of these results are contrary to the hyp. that chord a is d.
Prop. XIII. Theorem 169. A straight line perpendicular to a radius of a circle at its extremity is tangent to the circle.
Draw a O with centre at O, and radius 0(7. Through point G -draw line AB X 00. We then have : Given line AB ± radius 0(7 of O at (7.
To Prove AB tangent to the O.
Proof. 1. Let D be any point of AB except C.
2. Draw line 0J9; the
...n, OD > 00, (?) 3. Therefore, point D lies without the O.
4. Then, every point of AB except O lies without the O, and AB is tangent to the O. (§ 150) Prop. XIV. Theorem 170. (Converse of Prop. XIII.) A tangent to a circle is perpendicular to the radius drawn to the point of contact.
A a B Draw O with centre at 0. Draw line AB tangent to the O at (7.
Draw line 0(7. We then have : Given line AB tangent to O EO at (7, and radius 00, To Prove 00 ± AB, (00 is the shortest Hue from O to AB,) 76 PLANE GEOMETRY — BOOK II •171.


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