Elementary Geometry : Plane

Cover Elementary Geometry : Plane
Elementary Geometry : Plane
Mcmahon James
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Since BF is a tangent, the angle FBC is equal to the angle in the alternate segment BAG (76).
Therefore the angle in the segment BAG is equal to the given angle D.
Discussion. How many solutions are there to this problem ? How many solutions will there be if the state- ment of the problem is modified in the following manner : Through a given point on a circle, to draw a line that shall cut off a segment containing an angle equal to a given angle.
EXERCISES 1. All chords of a circle that touch a
... concentric circle are equal.
2. Through a given point draw a line so that the chord intercepted by a given circle shall be equal to a given line. [Use ex. 1 and art. 74. State the restrictions on the data when the point is within the circle ; also when the point is without or on the circle. ] 3. The part of any tangent intercepted by two parallel tangents subtends a right angle at the center of the circle.
4. If through the center of a circle two perpendicular lines are drawn to meet any tangent, then the tangents drawn from the two points of intersection are parallel.


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