...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 (JB Draw O with centre at O. Draw line AB tangent to the O at C. Draw line OC. We then have : Given...

...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 0 with centre at 0. Draw line AB tangent to the 0 at C Draw line OC. We then have : Given...

...equal. 169 Tangency. DEFINITIONS AND FIRST PRINCIPLES - 172 THEOREM 46. The tangent at any point of a circle is perpendicular to the radius drawn to the point of contact.' 174 COR. 1. One and only one tangent can be drawn to a circle at a given point on the circumference....

...from the center of a circle — that is, a line through a point within a circle — is a secant. (4) *A tangent to a circle is perpendicular to the radius drawn to the point of contact. Follows from (2). (5) *The perpendicular to a tangent at the point of contact passes through the center...

...XY is outside the circle. Therefore XY is tangent to the circle at P, by § 183. QED 185. COROLLARY 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For OP is the shortest line from 0 to XY, and is therefore _L to XY (§ 86); that is, XY is _L to OP....

...circumference, is called the point of tangency, or the point of contact. PROPOSITION XXX 101. Theorem: A tangent to a circle is perpendicular to the radius drawn to the point of contact; and conversely, a line drawn perpendicular to a radius at its outer end is a tangent to the circle....

...of the non-parallel sides of a trapezoid is parallel to the bases, and equal to half their sum. 3. A tangent to a circle is perpendicular to the radius drawn to the point of contact. 4. If any two chords be drawn through a fixed point within a circle the product of the segments of...

...these circles at A. Then by definition the spherical angle is measured by the angle TAS. But since a tangent to a circle is perpendicular to the radius drawn to the point of contact, AT and AS are perpendicular to OA, and hence TAS is the measure of the diedral angle T-OA-S or B-OA-C....

...these circles at A. Then by definition the spherical angle is measured by the angle TAS. But since a tangent to a circle is perpendicular to the radius drawn to the point of contact, AT and AS are perpendicular to OA, and hence TAS is the measure of the diedral angle T-OA-S or B-OA-C....

...0). 3. Find the equation of the normal to each of the circles of Ex. 2, through the given point 4. A tangent to a circle is perpendicular to the radius drawn to its point of contact. By means of this fact, derive the equation of the tangent to the circle (x —...