Chapter 4.7, Problem 5WE

To determine

To draw: a large scalene right triangle, and to draw the perpendicular bisectors of its three sides and tell whether they appear to meet in a point. To find the point.

Answer to Problem 5WE

The three perpendicular bisectors meet in a point $F$ and that point lies on the hypotenuse $AC$ of $\Delta ABC$ .

Explanation of Solution

The diagram is as follows:

  

Here, $\Delta ABC$ is right triangle with right angles at $B$ .

And $l,m,$ and $n$ are perpendicular bisectors of sides $AB,AC,$ and $BC$ respectively.

Use, the three perpendicular bisectors meet in a point $F$ and that point lies on the hypotenuse $AC$ of $\Delta ABC$ .