Geo_Book_Answers

1. incenter
LESSON 3.7
Because the station needs to be equidistant from
the paths, it will need to be on each of the angle
bisectors.
2. circumcenter
3. incenter
The center of the circular sink must be equidistant
from the three counter edges, that is, the incenter of
the triangle.
4. circumcenter
To find the point equidistant from three points,
find the circumcenter of the triangle with those
points as vertices.
5. Circumcenter. Find the perpendicular bisectors
of two of the sides of the triangle formed by the
classes. Locate the pie table where these two lines
intersect.
6.
7.
Stove
Fridge Sink
8. Yes, any circle with a larger radius would not
fit within the triangle. To get a circle with a larger
radius tangent to two of the sides would force the
circle to pass through the third side twice.
9. No, on an obtuse triangle the circle with the
largest side of the triangle as the diameter of the
circle creates the smallest circular region that
contains the triangle. The circumscribed circle of
an acute triangle does create the smallest circular
region that contains the triangle.
10. For an acute triangle, the circumcenter is
inside the triangle; for an obtuse triangle, the
circumcenter is outside the triangle. The
circumcenter of a right triangle lies on the
midpoint of the hypotenuse.
11. For an acute triangle, the orthocenter is inside
the triangle; for an obtuse triangle, the orthocenter
is outside the triangle. The orthocenter of a right
triangle lies on the vertex of the right angle.
12. The midsegment appears parallel to side MA
and half the length.
13. The base angles of the isosceles trapezoid
appear congruent.
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ANSWERS TO EXERCISES 43
Answers to Exercises