Ika, Imi, and Ariana are students at junior high school in Jakarta. On weekends, they plan to go on holiday together somewhere in the city. Before heading into the holidays, they will meet at one place so the distance between each of their homes will be the same.. If their home is shown by the map below, can we determine where they meet?
To determine where they meet, we can connect their homes with a line segment. So it will make a triangle whose third point is the location of the corner of Ika, Imi and Ariana.
The meeting place must have the same distance, so we can surmise that the meeting place of them is the focal point of a circle passing through the points where their home. Why? Because the distance between the center of the circle to any point on the circle is the same.
Outer circle of the triangle is a circle passing through the three triangle vertices. How do I determine the center point of the outer circle of the triangle? Outside the circle center point of the triangle is the intersection of the center lines of each side of the triangle. We can't manipulate it with the circumcircle of a triangle.
The circumcircle of a triangle is the circle
that passes through all vertices of the triangle and is the center of a circle
that circumscribes a triangle. The radius of the circle is the distance between
the circumcenter and any of the triangle's three vertices. It is found by
finding the midpoint of each leg of the triangle and constructing a line
perpendicular to that leg at its midpoint. Where all three lines intersect is
the circumcenter. So, the circumcenter is the point that forms the origin of a
circle in which all three vertices of the triangle lie on the circle.
And now i'll describe you how to drawing the circumcircle. Let's make it simple.
First step, start with a triangle ABC.
1. Find
the bisector of one of the triangle sides.
2. Repeat
for the another side.
(Optional step.) Repeat for the third side. This will convince you that
the three bisectors do, in fact, intersect at a single point. But two are
enough to find that point.
3. The
point where these two perpendiculars intersect is the triangle's circumcenter,
the center of the circle we desire.
(Note): This
point may lie outside the triangle. This is normal.
4. Place
the compass point on the intersection of the perpendiculars and set the compass
width to one of the points A, B or C. Draw a circle that will pass through all
three.
5. There you are! The circle drawn is the triangle's circumcircle, the only circle that will pass
through all three of its vertices.
As simple as that, see you!
