(a)
To construct: The three different equilateral
(a)
Answer to Problem 33PPS
The three different equilateral triangles and locate the circumcenter, incenter, centroid and the orthocentre is shown below.
Explanation of Solution
Construct the triangle and locate the points as shown in figure below.
(b)
To make: A conjecture about the relationship among four points concurrence of any equilateral triangle.
(b)
Answer to Problem 33PPS
The conjecture among the four points is that the location of circumcenter, incenter, centroid and othpcenter for an equilateral triangle are the same.
Explanation of Solution
Construct the triangle and locate the points as shown in figure below.
The conjecture among the four points is that the location of circumcenter, incenter, centroid and othpcenter for an equilateral triangle are the same.
(c)
To find: The points of concurrency.
(c)
Answer to Problem 33PPS
The point of concurrency is
Explanation of Solution
The y coordinate of the equilateral triangle is
The point of concurrence can be located using the centroid theorem.
It states that the centroid is
So, the location is
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