Name:
Date:
February
2008
Block:
Geometry: 6.9: GSP: Circumscribing and Inscribing Circles.
Teacher: Mrs. Chou
In your groups, finish the following definition of the term circle: A circle is the collection of points
In the circle drawn below, point O is the center, and
X on the circle to point O is equal to
called circle O.
OP is the radius. Therefore, the distance from any point
. We name a circle by its center, so that this circle could be
X
P
O
A tangent line is defined as a line in the plane of a circle that intersects the circle in ___________________,
called the point of tangency. Line l below is tangent to circle O at point X.
P
O
X
l
When each vertex of a triangle lies on a circle, we say that the circle is circumscribed about the triangle.
Circle O is circumscribed about ΔXDP below.
D
P
O
X
When each side of a triangle is tangent to a circle, we say that the circle is inscribed in the triangle. Below
circle H is inscribed in ΔFEG.
F
H
E
G
Your first mission: To discover a method to construct a circle that is circumscribed about a given triangle
using Geometer’s Sketchpad. Start by drawing a triangle on GSP. (Use the segment tool to do this!)
Your hints:
(i) Think about how the three vertices of the triangle relate to the center of the circumscribed circle.
(ii) Use this knowledge and the knowledge which you have gained from this most recent unit.
(iii) Once you find the center, you are on your way! Use the construct menu. It has many circle-constructing
options. Ask me if you need help at this point.
In the following space, clearly
printout to this worksheet.
explain how you constructed your circumscribed circle.
Staple your
Your second mission: To discover a method of constructing a circle that is inscribed in a triangle using
Geometer’s Sketchpad. Begin by opening a new sketch and drawing a triangle.
Your hints:
(i) Think about how the three sides of the triangle relate to the center of the inscribed circle.
(ii) A tangent line is perpendicular to the radius of the circle that connects to its point of tangency. For
example
OX ⊥ l.
D
O
P
l
X
(iii) Use this knowledge and the knowledge, which you have gained from this unit to construct your circle. If
you need help on how to do certain things on GSP, ask me.
In the following space, clearly
explain how you constructed your inscribed circle.