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## A triangular entranceway has walls with corner angles of 50°, 70°, and 60°. The designer wants to place a tall bronze sculpture on a round p

Question

A triangular entranceway has walls with corner angles of 50°, 70°, and 60°. The designer wants to place a tall bronze sculpture on a round pedestal in a central location equidistant from the three walls. How can the designer find where to place the sculpture?

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Mathematics
3 years
2021-08-26T12:42:56+00:00
2021-08-26T12:42:56+00:00 1 Answers
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## Answers ( )

Answer:

Look for the incenter and place it there.

Step-by-step explanation:

Since there are three angles of 50°, 70° and 60°. If the designer is to place a sculpture on a round central position equidistant from all three walls, then he is looking for the incenter.

The incenter is simply the point where the bisectors of all the three angles intersect. This point is also the center of the largest circle that can be drawn inside the triangle where it touches all three sides of the triangle. Definitely, if the incenter is the middle of the circle that touches all the three sides, then the incenter will be equidistant from the three walls due to the fact that radius will always be the same in a circle.

This is why, he is to look for the incenter.