PROPOSITIONS OF GEOMETRY Table 1d. Propositions of Geometry Machinery's Handbook, 31st Edition
64
A line tangent to a circle lies perpendicular (at right angles) to a radius drawn to meet it at the point of tangency.
90
Point of Tangency
The figure shows two ways that circles can be tangent. A line drawn through the center of each circle (the diameter) will pass through the point of tangency.
a
Two tangents drawn from a single point outside a circle will be equal in length ( a ), and the angles they make with the chord that connects the points of tangency ( A ) will be equal in measure. The figure shows this congruency.
A
A
a
d
The angle formed by a tangent and a chord drawn from the point of tangency measures one-half the central angle subtended by that chord. That is, B = A /2
A
B
d
The angle formed by a tangent and a chord drawn from the point of tangency has measure equal to the inscribed angle subtended
by the chord. That is, B = A .
A
B
b
c
a
All inscribed angles subtended by the same chord in a circle are congruent (equal in measure). In the figure, A , B , and C are subtended by chord cd , and so are equal in measure.
B
C
A
d
c
Referring to the figure, inscribed angle A and central angle B are subtended by the same arc. The measure of inscribed A is half the measure of central angle B . In the figure, A = B /2
A B
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