MathDB

Four masts stand on a flat horizontal piece of land at the vertices of a square

ABCD

. The height of the mast on

A

7

meters, of the mast on

B

13

meters, and of the mast on

C

15

meters. Within the square there is a point

P

on the ground equidistant from each of the tops of these three masts. (a) What length must the sides of the square be at least for this to be possible? (b) The distance from

P

to the top of the mast on

D

is equal to the distance from

P

to each of the tops of the three other masts. Calculate the height of the mast at

D

Problem Statement