...tangent, which has therefore, by art. 11, the same direction with the circumference at M. 120. Theorem. The tangent to a circle is perpendicular to the radius drawn to the point of contact. Demonstration. The radius OM = ON (fig. 58) is shorter than any other line, as OP, which can be drawn...

...Circle the Angle at the centre is double the Angle at the Circumference. (Euclid 20, 3.) - - 90 6*. A Tangent to a Circle is perpendicular to the Radius drawn to the Point of Contact. (Euclid, 3, 16.) - - ib. 7*. If two Tangents be drawn at the extremity of a Chord to intersect, the...

...straight line perpendicular to a radius at its extremity is a tangent to the circle. Conversely. Every tangent to a circle is perpendicular to the radius drawn to the point of contact. 1st. Let AB be perpen- F>s' ^ DE dicular to the radius CD, at its extremity D ; then we have to prove...

...perpendicular at the extremity of a radius is a tangent of the circumference ; and conversely, a tangent to the circle is perpendicular to the radius drawn to the point of contact. Let ABD be perpendicular to the radius CB, it shall touch the circle in the point B. For to show that...

...therefore tangent to it at the point D (D. 8). Therefore, etc. Cor. Conversely. — A tangent to the circle is perpendicular to the radius drawn to the point of contact. For any line, as CE, is greater than CF, or its equal CD; hence, CD, being the shortest line from C...

...The beginner, of course, must accept upon authority the meaning of the equations employed. To prove that the tangent to a circle is perpendicular to the radius drawn to the point of contact. — Let the axes be rectangular, and the center of the circle at the origin. Its equation is, in that...

...beginner, of course, must accept upon authority the meaning of the equations employed. To prove [hat the tangent to a circle is perpendicular to the radius drawn to the point of contact. — Let the axes be rectangular, and the center of the circle at the origin. Its equation is, in that...

...circle are derived from geometry, and will be found useful in their application to railway curves. 1 . A tangent to a circle is perpendicular to the radius drawn to the tangent point. Thus the tangent AC is perpendicular to the radius A M. 2. Two tangents drawn to a circle...

...which divides two sides of a triangle proportionally is parallel to the third side. 7. Prove that a tangent to a circle is perpendicular to the radius drawn to the point of contact. 8. Prove that parallel chords intercept upon the circumference equal arcs. ANCIENT HISTORY AND GEOGRAPHY....

...three parts proportional to the numbers 2, 4, and 3, and prove the principle involved. 7. Prove that a tangent to a circle is perpendicular to the radius drawn to the point of contact. 8. Prove that parallel chords intercept upon the circumference equal arcs. XIV. 1. Prove that two triangles...