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Example Questions
Example Question #41 : Plane Geometry
Figure NOT drawn to scale
The above figure shows Trapezoid , with
and
tangent to the circle.
; evaluate
.
Possible Answers:
Correct answer:
Explanation:
By the Same-Side Interior Angle Theorem, since ,
and
are supplementary - that is, their degree measures total
. Therefore,
is an inscribed angle, so the arc it intercepts,
, has twice its degree measure;
.
The corresponding major arc, , has as its measure
The measure of an angle formed by two tangents to a circle is equal to half the difference of those of its intercepted arcs:
Again, by the Same-Side Interior Angles Theorem, and
are supplementary, so
Iffy
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