...EB is tangent to the circle. (See 145, 147.) Proposition X. Theorem 157. A straight line, which is tangent to a circle, is perpendicular to the radius drawn to the point of contact. Det.: To prove that angle EAO is a right angle. Proof: Since EA is tangent to the circle at A, this...

...or other curve is a straight line which touches it at only one point, as ED and AC, Fig. 35. Every tangent to a circle is perpendicular to the radius drawn to the point of tangency. Thus ED is perpendicular to FD and AC to F B. Fig S4.—A Quadrant. Fig. S5.— Tangents....

...83). (11) The area of a triangle is equal to one-half of the product of its base and altitude. (12) A tangent to a circle is perpendicular to the radius drawn to the point of tangency. (13) An angle inscribed in a circle is measured by one-half the intercepted arc. In solving...

...often far removed from the axioms. For example, the proposition of Euclid asserting that a tangent of a circle is perpendicular to the radius drawn to the point of contact is hundreds of steps removed from the axioms on which it ultimately rests. Yet the theorem is as much...

...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....

...triangle is equal to a straight angle, (3) the base angles of an isosceles triangle are equal, (4) a tangent to a circle is perpendicular to the radius drawn to the point of contact, establish the following chain of theorems: (a) An exterior angle of a triangle is equal to the sum...

...a(t)-because the dot product a(t) • a'(t) is zero and this expresses the familiar fact that a tangent line to a circle is perpendicular to the radius drawn to the point of tangency (see Fig. 1-2). [In the previous sentence, picture a(t) as the arrow from the o'(t ) A (I)...

...triangle is equal to a straight angle, (3) The base angles of an isosceles triangle are equal, (4) A tangent to a circle is perpendicular to the radius drawn to the point of contact, establish the following chain of theorems: (a) An exterior angle of a triangle is equal to the sum...

...circle. A In a circle, two chords that are equidistant from the center of the circle are equal. AA tangent to a circle is perpendicular to the radius drawn to the point of tangency. A If a triangle is inscribed in a semicircle, then the triangle is a right triangle. A In...

...But when it is all done, one feels that Schoenberg reached some such conclusion as 'a straight line tangent to a circle is perpendicular to the radius drawn to the point of contact." Schoenberg's music is huge labor to demonstrate a simple enough theorem, namely, that if you employ...