# Find the coordinates of midpoint P of segment BC. Then Calculate the lengths of segments AP, BP, and CP. Is point P the circumcenter of triangle ABC? Is point A on the perpendicular bisector of...

Find the coordinates of midpoint P of segment BC. Then Calculate the lengths of segments AP, BP, and CP.

Is point P the circumcenter of triangle ABC?

Is point A on the perpendicular bisector of segment BC? (Always, never or sometimes)

Thank you for your help.

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Expert Answers

justaguide | Certified Educator

The coordinates of point B are (0, 2k) and that of point C are (2h, 0). The mid point of BC lies at P and its coordinates are `((0+2h)/2, (2k+0)/2)` = (h, k)

The length of AP is `sqrt(h^2 + k^2)` , the length of BP is `sqrt(h^2 + k^2)` , the length of CP is `sqrt(h^2 + k^2)`

The point P is the circum-center of triangle ABC.

Looking at the length of AP, PC and AC,

`AP^2 = h^2 + k^2` , `PC^2 = h^2 + k^2` and `AC = 4h^2`

Point A is on the perpendicular bisector of segment BC only when h = k.