...because the lines AB, DF, are parallel, the alternate angles D and B are equal (th. 12). But the angle B, formed by a tangent and chord, is measured by half the arc BD (th. 48) ; and the other angle at the circumference D is measured by half the arc BF (th. 49) ;...

...because the lines AB, DF, are parallel, the alternate angles D ami B are equal (th. 12). But the angle H, formed by a tangent and chord, is measured by half the arc ED (th. 48) ; and the other angle at the circumference D is measured by half the arc BF(th. 49) ; therefore...

...because the lines AB, DF, are parallel, the alternate angles D and B are equal (tb. 12). But the angle B, formed by a tangent and chord, Is measured by half the arc BD (th. 48) ; and the other angle at the circumference D is measured by half the arc BF (th. 49) ;...

...intercepted between the point of contact and the primitive plane is equal to its projection. § 199. PL 3. Fig. 1. At the point of contact conceive a plane...: hence, the triangle EDD' is isosceles, and ED is II i equal to ED'. But DE', in space, is the hypothenuse of a triangle of which DE is the base and...

...to the tangent at the common point must pass through the center of each. THEOREM XXXVIII. The angle formed by a tangent and chord is measured by half -the arc of that chord. Let AB be a tangent to a circle, and ACB CD a chord drawn from the point of ~7~~ contact...

...DF are parallel, the alternate angles DBA and BDF are equal ( B. I, Prop. xvn). But the angle DBA, formed by a tangent and chord, is measured by half the arc BD (B. lll, Prop. vn) ; and its equal angle BDF, being at the circumference, is measured by half the...

...(Cor. 1, of this Proposition.) 84 '.•. ELEMENTS OF GEOMETRY. PROPOSITION VI. L , y THEOREM. The angle formed by a tangent and chord is 'measured by half the arc of that chord. Let AB be a tangent, and CD a chord drawn from the point of contact C; then the angle...

...Any chords in a circle which are equally distant from the centre are equal to each other. 7. An angle formed by a tangent and chord is measured by half the arc of that chord. 8. An angle at the circumference of a circle, is measured by half the arc that subtends...

...the lines AB, DF, are parallel, the alternate angles D and B are equal (th. 13, BI). But the angle B, formed by a tangent and chord, is measured by half the arc BD (th. 8), and the other angle at the circumference D is measured by half the arc BF (th. 9) ; therefore...

...The radius OK bisects the arc AKB. Therefore AK is equal to KB. PROPOSITION XII.—THEOREM. An angle formed by a tangent and chord is measured by half the arc of that chord. The angle EDB beirig a right angle is measured by half the semi-circumference—that...