Desmos or GeoGebra Challenge
1) Construct \(\triangle ONE\) and three perpendicular bisectors. Find the point, \(P\), where the perpendicular bisectors intersect. Find \(PO\), \(PN\), and \(PE\). What do you notice?
2) Construct \(\triangle TWO\) and three angle bisectors. Find the point, \(A\), where the angle bisectors intersect. Find the distance from \(A\) to \(\overline{TW}\), \(A\) to \(\overline{WO}\), and \(A\) to \(\overline{TO}\). What do you notice?
3) Construct \(\triangle TRI\) and three medians. Find the point, (\M\), where the three medians intersect. Find \(TM\) and the distance from \(M\) to the midpoint of \(\overline{RI}\). What do you notice? What do you wonder?
1) Construct \(\triangle ONE\) and three perpendicular bisectors. Find the point, \(P\), where the perpendicular bisectors intersect. Find \(PO\), \(PN\), and \(PE\). What do you notice?
2) Construct \(\triangle TWO\) and three angle bisectors. Find the point, \(A\), where the angle bisectors intersect. Find the distance from \(A\) to \(\overline{TW}\), \(A\) to \(\overline{WO}\), and \(A\) to \(\overline{TO}\). What do you notice?
3) Construct \(\triangle TRI\) and three medians. Find the point, (\M\), where the three medians intersect. Find \(TM\) and the distance from \(M\) to the midpoint of \(\overline{RI}\). What do you notice? What do you wonder?